| Title |
|---|
| 2nd-Countable Topological Space |
| Abelian Group |
| Accumulation Value of Net with Directed Index Set |
| Adjunction Topological Space Obtained by Attaching Topological Space via Map to Topological Space |
| Affine Combination of Possibly-Non-Affine-Independent Set of Base Points on Real Vectors Space |
| Affine Map from Affine Set Spanned by Possibly-Non-Affine-Independent Set of Base Points on Real Vectors Space |
| Affine Map from Convex Set Spanned by Possibly-Non-Affine-Independent Set of Base Points on Real Vectors Space |
| Affine Set Spanned by Possibly-Non-Affine-Independent Set of Base Points on Real Vectors Space |
| Affine Simplex |
| Affine Subset of Real Vectors Space |
| Affine-Independent Set of Points on Real Vectors Space |
| Algebra over Field |
| Antisymmetric-Tensors Space w.r.t. Field and \(k\) Same Vectors Spaces and Vectors Space over Field |
| Antisymmetrization of Tensor w.r.t. Some Arguments |
| Ascending Sequence of Barycenters of Faces of Affine Simplex |
| Ascending Sequence of Faces of Affine Simplex |
| Associates of Element of Commutative Ring |
| Banach Space |
| Barycenter of Affine Simplex |
| Barycentric Subdivision of Simplicial Complex |
| Basis of Module |
| Basis of Topological Space |
| Bijection |
| Borel \(\sigma\)-Algebra of Topological Space |
| Boundary of Subset of Topological Space |
| Bounded Map Between Normed Vectors Spaces |
| \(C^\infty\) \((2, 0)\)-Tensors Field Induced by Riemannian Metric over \(C^\infty\) Manifold with Boundary |
| \(C^\infty\) Covering Map |
| \(C^\infty\) Embedding |
| \(C^\infty\) Immersion |
| \(C^\infty\) Locally Trivial Surjection of Rank \(k\) |
| \(C^\infty\) Manifold |
| \(C^\infty\) Manifold with Boundary |
| \(C^\infty\) Map Induced from \(C^\infty\) Map from Finite-Product \(C^\infty\) Manifold with Boundary by Fixing Some Domain Components Based on Point |
| \(C^\infty\) Map Projected from \(C^\infty\) Map from Finite-Product \(C^\infty\) Manifold with Boundary by Fixing Domain Components Except \(j\)-th Based on Point |
| \(C^\infty\) Submersion |
| \(C^\infty\) Trivializing Open Subset and \(C^\infty\) Local Trivialization |
| \(C^\infty\) Vectors Bundle of Rank \(k\) |
| '\(C^\infty\) Vectors Bundles - \(C^\infty\) Vectors Bundle Homomorphisms' Isomorphism from Tangent Vectors Bundle onto Cotangent Vectors Bundle w.r.t. Riemannian Metric |
| \(C^\infty\) Vectors Field Along \(C^\infty\) Curve |
| \(C^\infty\) Vectors Field over \(C^\infty\) Manifold with Boundary |
| \(C^\infty\) Vectors Subbundle of Rank \(k\) of \(C^\infty\) Vectors Bundle of Rank \(k'\) |
| \(C^\infty\) \((p, q)\)-Tensors Bundle over \(C^\infty\) Manifold with Boundary |
| \(C^\infty\) \((p, q)\)-Tensors Field over \(C^\infty\) Manifold with Boundary |
| \(C^\infty\) \(q\)-Covectors Bundle over \(C^\infty\) Manifold with Boundary |
| Canonical \(C^\infty\) Atlas for Finite-Dimensional Real Vectors Space |
| Canonical Topology for Finite-Dimensional Complex Vectors Space |
| Canonical Topology for Finite-Dimensional Real Vectors Space |
| Canonical 'Vectors Spaces - Linear Morphisms' Isomorphism Between Finite-Dimensional Vectors Space and Its Covectors Space w.r.t. Original Space Basis |
| Canonical 'Vectors Spaces - Linear Morphisms' Isomorphism Between Finite-Dimensional Vectors Space and Its Double Dual Space |
| Canonical 'Vectors Spaces - Linear Morphisms' Isomorphism Between \((p, q)\)-Tensors Space at Point on \(C^\infty\) Manifold with Boundary and Tensors Space w.r.t. Real Numbers Field and \(p\) Cotangent Vectors Spaces and \(q\) Tangent Vectors Spaces and Field |
| Category |
| %Category Name% Automorphism |
| %Category Name% Isomorphism |
| Cauchy Sequence on Metric Space |
| Center of Group |
| Centralizer of Element on Group |
| Chain in Set |
| Characteristic of Ring |
| \(r\)-Open-Ball Chart Around Point on \(C^\infty\) Manifold with Boundary |
| \(r\)-Open-Half-Ball Chart Around Point on \(C^\infty\) Manifold with Boundary |
| Chart on \(C^\infty\) Manifold |
| Chart on \(C^\infty\) Manifold with Boundary |
| Chart on Topological Manifold |
| Chart on Topological Manifold with Boundary |
| \(C^k\) Map Between Arbitrary Subsets of \(C^\infty\) Manifolds with Boundary, Where \(k\) Includes \(\infty\) |
| Closed Upper Half Euclidean \(C^\infty\) Manifold with Boundary |
| Closed Upper Half Euclidean Topological Space |
| Closed Subset of Topological Space |
| Closure of Subset of Topological Space |
| Compact Subset of Topological Space |
| Compact Topological Space |
| Compactly-Supported Map from Topological Space into Ring or Module |
| Complementary Subspace of Vectors Subspace |
| Complete Metric Space |
| Complex Conjugate of Complex Matrix |
| Complex Conjugate of Complex Vectors Space |
| Complex Euclidean Inner Product on Complex Euclidean Vectors Space |
| Complex Euclidean Metric on Complex Euclidean Set |
| Complex Euclidean Norm on Complex Euclidean Vectors Space |
| Complex Euclidean Topological Space |
| Complex Euclidean Vectors Space |
| Complex-Conjugate-Linear Map |
| Complex-Euclidean-Normed Complex Euclidean Vectors Space |
| Composition of Maps |
| Congruence on Category |
| Conjugate Subgroup of Subgroup by Element |
| Conjugation for Group by Element |
| Connected Topological Component |
| Connected Topological Space |
| Continuous Embedding |
| Continuous, Normed Vectors Spaces Map |
| Continuous, Topological Spaces Map |
| Contractible Topological Space |
| Contravariant Functor |
| Convergence of Map from Topological Space Minus Point into Topological Space w.r.t. Point |
| Convergence of Net with Directed Index Set |
| Convergence of Sequence on Metric Space |
| Convex Combination of Possibly-Non-Affine-Independent Set of Base Points on Real Vectors Space |
| Convex Set Spanned by Possibly-Non-Affine-Independent Set of Base Points on Real Vectors Space |
| Convex Subset of Real Vectors Space |
| Cotangent Vectors Bundle over \(C^\infty\) Manifold with Boundary |
| Covariant Functor |
| Covectors (Dual) Space of Vectors Space |
| Covering Map |
| Curve on Topological Space |
| Cyclic Group by Element |
| Deformation Retract of Topological Space |
| Deformation Retraction |
| Dense Subset of Topological Space |
| Derivation at Point of \(C^k\) Functions |
| Derivative of Normed Vectors Spaces Map |
| Derivative of Real-1-Parameter Family of Vectors in Finite-Dimensional Real Vectors Space |
| Determinant of Finite-Dimensional Vectors Space Endomorphism |
| Determinant of Square Matrix over Ring |
| Dichotomically Disjoint Set of Sets |
| Diffeomorphism Between Arbitrary Subsets of \(C^\infty\) Manifolds with Boundary |
| Differential of \(C^\infty\) Map Between \(C^\infty\) Manifolds with Boundary at Point |
| Dihedral Group |
| Dimension of Vectors Space |
| Direct Product of Structures |
| Direct Sum of Modules |
| Directed Set |
| Directional Derivative |
| Disjoint Union Topology |
|
| Dual Basis for Covectors (Dual) Space of Basis for Finite-Dimensional Vectors Space |
Embedded Submanifold with Boundary of \(C^\infty\) Manifold with Boundary |
| Equivalence Relation on Set |
| Equivalence Relation on Norms on Vectors Space |
| Euclidean \(C^\infty\) Manifold |
| Euclidean Inner Product on Euclidean Vectors Space |
| Euclidean Metric on Euclidean Set |
| Euclidean Norm on Euclidean Vectors Space |
| Euclidean Topological Space |
| Euclidean Topology |
| Euclidean Vectors Space |
| Euclidean-Normed Euclidean Vectors Space |
| Euler's Totient Function |
| Exhaustion Function on Topological Space |
| Exhaustion of Topological Space by Compact Subsets |
| Extended Field of Field |
| Exterior Derivative of \(C^\infty\) Function over \(C^\infty\) Manifold with Boundary |
| Face of Affine Simplex |
| Face of Orientated Affine Simplex |
| Field |
| Field Generated by Subset of Superfield over Subfield |
| %Field Name% Vectors Space |
| Final Map Between Directed Sets |
| 'Finite Simplicial Complexes - Simplicial Maps' Category |
| 'Finite Simplicial Complexes - Simplicial Maps' Category to Top Functor |
| Finite-Open-Sets-Sequence-Connected Pair of Open Sets |
| Finite-Product \(C^\infty\) Manifold with Boundary |
| Finite-Product Hilbert Space |
| Finite-Product Inner Product |
| Finitely-Generated Module |
| Free Vectors Space on Set |
| Frobenius Endomorphism for Commutative Ring with Prime Characteristic |
| Frobenius Matrix Norm |
| Function |
| Function over \(C^\infty\) Manifold with Boundary |
| \(G_\delta\) Subset of Topological Space |
| General Linear Group of Finite-Dimensional Real Vectors Space |
| General Linear Group of Vectors Space |
| General Linear Lie Algebra, \(\mathfrak{gl} (V)\) |
| Generator of Module |
| Germ of \(C^k\) Functions at Point |
| Global Differential of \(C^\infty\) Map Between \(C^\infty\) Manifolds with Boundary |
| Gradient of \(C^\infty\) Function over Riemannian Manifold with Boundary |
| Gram-Schmidt Orthonormalization of Countable Subset of Vectors Space with Inner Product |
| Graph of Map |
| Greatest Common Divisors Domain |
| Greatest Common Divisors of Subset of Commutative Ring |
| Group |
| Group Left Action |
| Group Left Action That Corresponds to Group Right Action |
| Group Right Action |
| Group Right Action That Corresponds to Group Left Action |
| Group as Direct Sum of Finite Number of Normal Subgroups |
| Hausdorff Topological Space |
| Hermitian Conjugate of Complex Matrix |
| Hermitian Matrix |
| Hilbert Space |
| Homeomorphism |
| Homotopic Maps |
| Homotopy Equivalence |
| Ideal of Lie Algebra |
| Ideal of Ring |
| Immersed Submanifold with Boundary of \(C^\infty\) Manifold with Boundary |
| Injection |
| Inner Product on Real or Complex Vectors Space |
| Integers Modulo Natural Number Group |
| Integers Modulo Natural Number Ring |
| Integers Modulo Prime Number Field |
| Integers Ring |
| Integral Domain |
| Interior \(C^\infty\) Manifold of \(C^\infty\) Manifold with Boundary |
| Interior Multiplication of Antisymmetric-Tensor by Vector |
| Interior Multiplication of Tensor by Vector |
| Interior of Subset of Topological Space |
| Intersection of Set |
| Inverse of Square Matrix over Ring |
| Inverse of Subset of Group |
| Irreducible Element of Commutative Ring |
| \(J\)-Half-Slice of Chart Domain w.r.t. Point |
| \(J\)-Slice of Chart Domain w.r.t. Point |
| Kernel of Group Homomorphism |
| Kernel of Linear Map |
| Kernel of Ring Homomorphism |
| Latin Square of Finite Set |
| Least Common Multiples of Subset of Commutative Ring |
| Left R-Module |
| Left or Right Coset of Subgroup by Element of Group |
| Lie Algebra |
| Lie Bracket (Commutator) of \(C^\infty\) Vectors Fields on \(C^\infty\) Manifold with Boundary |
| Lie Group |
| Lie Subgroup |
| Lift of Continuous Map by Covering Map |
| Limit of Normed Vectors Spaces Map at Point |
| Linear Map |
| Linearly Independent Subset of Module |
| Linearly-Ordered Set |
| Lipschitz Map Between Metric Spaces |
| Lipschitz Map from Subset of Normed Vectors Space into Normed Vectors Space |
| Local \(C^\infty\) Frame on \(C^\infty\) Vectors Bundle |
| Locally Compact Topological Space |
| Locally Connected Topological Space |
| Locally Finite Set of Subsets of Topological Space |
| Locally Path-Connected Topological Space |
| Locally Topologically Closed Upper Half Euclidean Topological Space |
| Locally Topologically Euclidean Topological Space |
| Locally Trivial Surjection of Rank \(k\) |
| Map |
| Map Between Arbitrary Subsets of \(C^\infty\) Manifolds with Boundary \(C^k\) at Point, Where \(k\) Excludes \(0\) and Includes \(\infty\) |
| Map Between Arbitrary Subsets of \(C^\infty\) Manifolds with Boundary Locally Diffeomorphic at Point |
| Map Between Arbitrary Subsets of Euclidean \(C^\infty\) Manifolds \(C^k\) at Point, Where \(k\) Excludes \(0\) and Includes \(\infty\) |
| Map from Open Subset of Euclidean \(C^\infty\) Manifold into Subset of Euclidean \(C^\infty\) Manifold \(C^k\) at Point, Where \(k\) Excludes \(0\) and Includes \(\infty\) |
| Map-Related Vectors Fields Pair for \(C^\infty\) Map Between \(C^\infty\) Manifolds with Boundary |
| Maps Homotopic Relative to Subset of Domain |
| Matrix Norm Induced by Vector Norms |
| Maximal Atlas for Topological Manifold |
| Maximal Atlas for Topological Manifold with Boundary |
| Maximal Element of Set |
| Maximal Ideal of Ring |
| Maximal Simplex in Simplicial Complex |
| Measurable Map Between Measurable Spaces |
| Measurable Map from Measurable Space into Topological Space |
| Measurable Space |
| Measurable Subspace |
| Metric |
| Metric Induced by Norm on Real or Complex Vectors Space |
| Metric Space |
| 'Metric Space' Isometry |
| Metric Subspace |
| Module as Direct Sum of Finite Number of Submodules |
| Monoid |
| Morphism |
| Motion |
| Multilinear Map |
| Neighborhoods Basis at Point on Topological Space |
| Neighborhood of Point on Topological Space |
| Neighborhood of Subset |
| Net with Directed Index Set |
| Non-Degenerate Hermitian Matrix |
| Norm Induced by Inner Product on Real or Complex Vectors Space |
| Norm on Real or Complex Vectors Space |
| Normal Subgroup of Group |
| Normal Topological Space |
| Normalizer of Subgroup on Group |
| Normed Covectors (Dual) Space of Normed Vectors Space |
| Normed Vectors Space |
| 'Normed Vectors Space' Isometry |
| Normed Vectors Spaces Map Continuous at Point |
| 'Normed Vectors Spaces - Linear Isometries' Category |
| Nowhere Dense Subset of Topological Space |
| Open Ball Around Point on Metric Space |
| Open Map |
| Open Subset of Topological Space |
| Open Submanifold with Boundary of \(C^\infty\) Manifold with Boundary |
| Order of Element of Group |
| Ordered Pair |
| Orientated Affine Simplex |
| Orientable \(C^\infty\) Manifold with Boundary |
| Orientation of \(C^\infty\) Manifold with Boundary |
| Orientation of Finite-Dimensional Real Vectors Space |
| Orientation of Point on \(C^\infty\) Manifold with Boundary |
| Orientation-Preserving Local Diffeomorphism Between Oriented \(C^\infty\) Manifolds with Boundary |
| Orientation-Reversing Local Diffeomorphism Between Oriented \(C^\infty\) Manifolds with Boundary |
| Oriented \(C^\infty\) Manifold with Boundary |
| Orthogonal Complement of Subset of Vectors Space with Inner Product |
| Orthogonal Linear Map |
| Orthogonal Matrix |
| Orthogonal Projection from Vectors Space with Inner Product into Vectors Subspace |
| Orthonormal Subset of Vectors Space with Inner Product |
| Partially-Ordered Set |
| Partition of Unity Subordinate to Open Cover of Topological Space |
| Path-Connected Topological Component |
| Path-Connected Topological Space |
| Permutation of Sequence |
| Polish Space |
| Polynomial Extended over Extended Field |
| Polynomials Ring over Commutative Ring |
| Positive-Definite Hermitian Matrix |
| Power Set of Set |
| Primitive n-th Root of 1 on Field |
| Principal Ideal of Ring |
| Product Module |
| Product Vectors Space |
| Projection from Vectors Space into Vectors Subspace |
| Projection of Vector into Vectors Subspace w.r.t. Complementary Subspace |
| Proper Map |
| Properly Embedded Submanifold with Boundary of \(C^\infty\) Manifold with Boundary |
| Principal Integral Domain |
| Product Map |
| Product Set |
| Product Topological Space |
| Product Topology |
| Pullback of \((0, q)\)-Tensors at Point by \(C^\infty\) Map Between \(C^\infty\) Manifolds with Boundary |
| Pullback of \(q\)-Covectors at Point by \(C^\infty\) Map Between \(C^\infty\) Manifolds with Boundary |
| Quotient Category |
| Quotient Group of Group by Normal Subgroup |
| Quotient Lie Algebra of Lie Algebra by Ideal of Lie Algebra |
| Quotient Map |
| Quotient Ring of Ring by Ideal |
| Quotient Set |
| Quotient Topology on Set with Respect to Map |
| Quotient Vectors Space of Vectors Space by Vectors Subspace |
| Rank of \(C^\infty\) Map Between \(C^\infty\) Manifolds with Boundary at Point |
| Rank of Linear Map Between Vectors Spaces |
| Rank of Matrix over Ring |
| Regular Domain of \(C^\infty\) Manifold with Boundary |
| Relation |
| Representatives Set of Quotient Set |
| Restricted \(C^\infty\) Vectors Bundle |
| Retract of Topological Space |
| Retraction |
| Riemannian Manifold with Boundary |
| Riemannian Metric over \(C^\infty\) Manifold with Boundary |
| Ring |
| %Ring Name% Matrices Space |
| %Ring Name% Module |
| Regular Topological Space |
| Reversed Operator Group of Group |
| Root of Polynomial in Polynomials Ring over Commutative Ring |
| Rough Section of Continuous Surjection |
| Rough Vectors Field over \(C^\infty\) Manifold with Boundary |
| Rough \(q\)-Form over \(C^\infty\) Manifold with Boundary |
| Rough \((p, q)\)-Tensors Field over \(C^\infty\) Manifold with Boundary |
| Same-Length Multi-Dimensional Array Antisymmetrized with Respect to Set of Indexes |
| Same-Length Multi-Dimensional Array Symmetrized with Respect to Set of Indexes |
| Schauder Basis for Normed Vectors Space |
| Section Along Subset of Codomain of Continuous Surjection |
| Section of Continuous Surjection |
| Separable Topological Space |
| Sequence |
| Set Elements Minus Set |
| \(\sigma\)-Algebra Induced on Codomain of Map from Measurable Space |
| \(\sigma\)-Algebra of Set |
| \(\sigma\)-Algebra of Set Generated by Set of Subsets |
| Simple Group |
| Simplex Boundary of Affine Simplex |
| Simplex Interior of Affine Simplex |
| Simplicial Complex |
| Simplicial Map |
| Simply Connected Topological Space |
| Skewed Dihedral Group |
| Slicing Map on Euclidean Set |
| Slicing-and-Halving Map on Euclidean Set |
| Standard Basis for Tangent Vectors Space at Point on \(C^\infty\) Manifold with Boundary w.r.t. Chart |
| Standard Simplex |
| Standard Topology for \(\mathbb{R}^n\) |
| Star of Vertex in Simplicial Complex |
| Structure |
| %Structure Kind Name% Endomorphism |
| %Structure Kind Name% Homomorphism |
| Subbasis of Topological Space |
| Subgroup Generated by Subset of Group |
| Subnet of Net with Directed Index Set |
| Subset of \(C^\infty\) Manifold with Boundary That Satisfies Local-Slice Condition |
| Subset of \(C^\infty\) Manifold with Boundary That Satisfies Local-Slice-or-Half-Slice Condition |
| Subspace Topology of Subset of Topological Space |
| Subspace \(\sigma\)-Algebra of Subset of Measurable Space |
| Sum of Finite Number of Subsets of Module |
| Support of Map from Topological Space into Ring or Module |
| Surjection |
| Sylow p-Subgroup of Group |
| Symmetric Subset of Group |
| Symmetrization of Tensor w.r.t. Some Arguments |
| Tangent Vector |
| Tangent Vectors Bundle over \(C^\infty\) Manifold with Boundary |
| Tangent Vectors Space at Point on \(C^\infty\) Manifold with Boundary |
| Tensor Product of Tensors |
| Tensor Product of \(k\) Vectors Spaces over Field |
| Tensors Space w.r.t. Field and \(k\) Vectors Spaces and Vectors Space over Field |
| Top Category |
| Top-Covectors Space of Finite-Dimensional Vectors Space |
| \(Top^*\) Category |
| \(Top^2\) Category |
| Topological Connected-Ness of 2 Points |
| Topological Group |
| Topological Manifold |
| Topological Manifold with Boundary |
| Topological Path |
| Topological Path-Connected-Ness of 2 Points |
| Topological Space |
| Topological Spaces Map Continuous at Point |
| Topological Subspace |
| Topological Sum |
| Topology |
| Topology Induced by Metric |
| Trace of Finite-Dimensional Vectors Space Endomorphism |
| Transitive Closure of Subset |
| Transpose of Matrix |
| Trivializing Open Subset and Local Trivialization |
| Uniformly Convergent Sequence of Maps from Topological Space into Metric Space |
| Union of Set |
| Unique Factorization Domain |
| Unitary Matrix |
| Units of Ring |
| Vandermonde Determinant |
| Vectors Bundle of Rank \(k\) |
| Vectors Subbundle of Rank \(k\) of Vectors Bundle of Rank \(k'\) |
| Vectors Subspace Generated by Subset of Vectors Space |
| Velocity of \(C^\infty\) Curve at Point on \(C^\infty\) Manifold with Boundary |
| Vertex in Simplicial Complex |
| Vertex of Affine Simplex |
| Wedge Product |
| Wedge Product of Multicovectors |
| Wedge Sum of Pointed Maps |
| Wedge Sum of Pointed Sets |
| Wedge Sum of Pointed Topological Spaces |
| Well-Ordered Set |
| hTop Category |
| \((j, l)\)-Cofactor of Square Matrix |
| \((j, l)\)-Minor of Matrix |
| m-Cycle on n-Symmetric Group |
| n-Alternating Group |
| \(n\)-Cube Centered at \(p\) with Edges-Length \(l\) with Indexes \(B\) |
| \(n\)-Disk Centered at \(p\) with Radius \(r\) with Indexes \(B\) |
| n-Symmetric Group |
| p-Group |
| \((p, q)\)-Tensors Space at Point on \(C^\infty\) Manifold with Boundary |
| \(q\)-Covectors Space at Point on \(C^\infty\) Manifold with Boundary |
| \(q\)-Form over \(C^\infty\) Manifold with Boundary |
| \(r'\)-\(r\)-Open-Balls Charts Pair Around Point on \(C^\infty\) Manifold with Boundary |
| \(r'\)-\(r\)-Open-Half-Balls Charts Pair Around Point on \(C^\infty\) Manifold with Boundary |
