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 Topological Space |
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-Normed Euclidean Vectors Space |
Euclidean \(C^\infty\) Manifold |
Euclidean Inner Product on Euclidean Vectors Space |
Euclidean Metric |
Euclidean Norm on Euclidean Vectors Space |
Euclidean Topological Space |
Euclidean Topology |
Euclidean Vectors Space |
Euler's Totient Function |
Exhaustion Function on Topological Space |
Exhaustion of Topological Space by Compact Subsets |
Extended Field of Field |
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 |
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 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 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 Subspace |
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 Vectors Space |
Normed Vectors Spaces Map Continuous at Point |
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 |
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 |
Quotient Category |
Quotient Group of Group by Normal Subgroup |
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 Sub-'Vectors Space' |
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 |
Union of Set |
Unique Factorization Domain |
Unitary Matrix |
Units of Ring |
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 |