1: A List of Definitions

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The list of definitions discussed so far in this site

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Topics

About: definitions

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: The Definitions List

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Starting Context

• Nothing

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Target Context

• The reader will know the list of definitions discussed so far in this cite and can jump to the page of any of them, which (the page) has a description of the definition.

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Orientation

There is a list of propositions discussed so far in this site.

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Main Body

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1: The Definitions List

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
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
$C^{\mathrm{\infty }}$ Embedding
$C^{\mathrm{\infty }}$ Immersion
$C^{\mathrm{\infty }}$ Locally Trivial Surjection of Rank $k$
$C^{\mathrm{\infty }}$ Manifold
$C^{\mathrm{\infty }}$ Manifold with Boundary
$C^{\mathrm{\infty }}$ Map Induced from $C^{\mathrm{\infty }}$ Map from Finite-Product $C^{\mathrm{\infty }}$ Manifold with Boundary by Fixing Some Domain Components Based on Point
$C^{\mathrm{\infty }}$ Map Projected from $C^{\mathrm{\infty }}$ Map from Finite-Product $C^{\mathrm{\infty }}$ Manifold with Boundary by Fixing Domain Components Except $j$-th Based on Point
$C^{\mathrm{\infty }}$ Submersion
$C^{\mathrm{\infty }}$ Trivializing Open Subset and $C^{\mathrm{\infty }}$ Local Trivialization
$C^{\mathrm{\infty }}$ Vectors Bundle of Rank $k$
$C^{\mathrm{\infty }}$ Vectors Field Along $C^{\mathrm{\infty }}$ Curve
$C^{\mathrm{\infty }}$ Vectors Field on $C^{\mathrm{\infty }}$ Manifold with Boundary
Canonical $C^{\mathrm{\infty }}$ Atlas for Finite-Dimensional Real 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 Tensors Space at Point on $C^{\mathrm{\infty }}$ 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
Chart Ball Around Point on $C^{\mathrm{\infty }}$ Manifold with Boundary
Chart Half Ball Around Point on $C^{\mathrm{\infty }}$ Manifold with Boundary
Chart on $C^{\mathrm{\infty }}$ Manifold
Chart on $C^{\mathrm{\infty }}$ Manifold with Boundary
Chart on Topological Manifold
Chart on Topological Manifold with Boundary
$C^k$ Map Between Arbitrary Subsets of $C^{\mathrm{\infty }}$ Manifolds with Boundary, Where $k$ Includes $\mathrm{\infty }$
Closed Upper Half Euclidean $C^{\mathrm{\infty }}$ Manifold with Boundary
Closed Upper Half Euclidean Topological Space
Closed Set
Closure of Subset of Topological Space
Compact Subset of Topological Space
Compact Topological Space
Complementary Subspace of Vectors Subspace
Complete Metric 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 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
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
Dichotomically Disjoint Set of Sets
Diffeomorphism Between Arbitrary Subsets of $C^{\mathrm{\infty }}$ Manifolds with Boundary
Differential of $C^{\mathrm{\infty }}$ Map Between $C^{\mathrm{\infty }}$ 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 $C^{\mathrm{\infty }}$ Manifold with Boundary
Equivalence Relation on Set
Equivalence Relation on Norms on Vectors Space
Euclidean-Normed Euclidean Vectors Space
Euclidean $C^{\mathrm{\infty }}$ 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 $C^{\mathrm{\infty }}$ Manifold with Boundary
Finitely-Generated Module
Free Vectors Space on Set
Frobenius Endomorphism for Commutative Ring with Prime Characteristic
Frobenius Matrix Norm
Function
Function over $C^{\mathrm{\infty }}$ Manifold with Boundary
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 $C^{\mathrm{\infty }}$ Map Between $C^{\mathrm{\infty }}$ Manifolds with Boundary
Graph of Map
Greatest Common Divisors Domain
Greatest Common Divisors of Subset of Commutative Ring
Group
Group Action
Group as Direct Sum of Finite Number of Normal Subgroups
Hausdorff Topological Space
Hilbert Space
Homeomorphism
Homotopic Maps
Homotopy Equivalence
Ideal of Ring
Immersed Submanifold with Boundary of $C^{\mathrm{\infty }}$ 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 $C^{\mathrm{\infty }}$ Manifold of $C^{\mathrm{\infty }}$ Manifold with Boundary
Interior of Subset of Topological Space
Intersection of Set
Irreducible Element of Commutative Ring
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 $C^{\mathrm{\infty }}$ Vectors Fields on $C^{\mathrm{\infty }}$ Manifold with Boundary
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
Local $C^{\mathrm{\infty }}$ Frame on $C^{\mathrm{\infty }}$ 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 $C^{\mathrm{\infty }}$ Manifolds with Boundary $C^k$ at Point, Where $k$ Excludes $0$ and Includes $\mathrm{\infty }$
Map Between Arbitrary Subsets of $C^{\mathrm{\infty }}$ Manifolds with Boundary Locally Diffeomorphic at Point
Map Between Arbitrary Subsets of Euclidean $C^{\mathrm{\infty }}$ Manifolds $C^k$ at Point, Where $k$ Excludes $0$ and Includes $\mathrm{\infty }$
Map Continuous at Point
Map from Open Subset of Euclidean $C^{\mathrm{\infty }}$ Manifold into Subset of Euclidean $C^{\mathrm{\infty }}$ Manifold $C^k$ at Point, Where $k$ Excludes $0$ and Includes $\mathrm{\infty }$
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
Monoid
Morphism
Motion
Multilinear Map
Neighborhood Basis at Point
Neighborhood of Point
Neighborhood of Subset
Net with Directed Index Set
Norm Induced by Inner Product on Real or Complex Vectors Space
Normal Subgroup of Group
Normal Topological Space
Normalizer of Subgroup on Group
Normed Vectors Spaces Map Continuous at Point
Nowhere Dense Subset of Topological Space
Open Ball Around Point on Metric Space
Open Set
Open Submanifold with Boundary of $C^{\mathrm{\infty }}$ Manifold with Boundary
Order of Element of Group
Ordered Pair
Orientated Affine Simplex
Orthogonal Linear Map
Partially-Ordered Set
Path-Connected Topological Component
Path-Connected Topological Space
Permutation of Sequence
Polish Space
Polynomial Extended over Extended Field
Polynomials Ring over Commutative Ring
Power Set of Set
Primitive n-th Root of 1 on Field
Principal Ideal of Ring
Product Module
Product Vectors Space
Projection of Vector into Vectors Subspace w.r.t. Complementary Subspace
Proper Map
Properly Embedded Submanifold with Boundary of $C^{\mathrm{\infty }}$ Manifold with Boundary
Principal Integral Domain
Product Map
Product Set
Product Topological Space
Product Topology
Pullback of $(0,q)$-Tensors at Point by $C^{\mathrm{\infty }}$ Map Between $C^{\mathrm{\infty }}$ 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'
Regular Domain of $C^{\mathrm{\infty }}$ Manifold with Boundary
Relation
Representatives Set of Quotient Set
Restricted $C^{\mathrm{\infty }}$ Vectors Bundle
Retract of Topological Space
Retraction
%Ring Name% Module
Norm on Real or Complex Vectors Space
Normed Vectors Space
Regular Topological Space
Reversed Operator Group of Group
Ring
Root of Polynomial in Polynomials Ring over Commutative Ring
Same-Length Multi-Dimensional Array Antisymmetrized with Respect to Set of Indexes
Same-Length Multi-Dimensional Array Symmetrized with Respect to Set of Indexes
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 $C^{\mathrm{\infty }}$ 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
Sub-'Vectors Space' Generated by Subset of Vectors Space
Subbasis of Topological Space
Subgroup Generated by Subset of Group
Subnet of Net with Directed Index Set
Subspace Topology of Subset of Topological Space
Subspace $\sigma$-Algebra of Subset of Measurable Space
Support of Map from Topological Space into Field
Surjection
Sylow p-Subgroup of Group
Symmetrization of Tensor w.r.t. Some Arguments
Tangent Vector
Tangent Vectors Bundle over $C^{\mathrm{\infty }}$ Manifold with Boundary
Tangent Vectors Space at Point on $C^{\mathrm{\infty }}$ 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
$To{p}^{\ast }$ Category
$To{p}^2$ Category
Topological Connected-Ness of 2 Points
Topological Manifold
Topological Manifold with Boundary
Topological Path
Topological Path-Connected-Ness of 2 Points
Topological Space
Topological Subspace
Topological Sum
Topology
Topology Induced by Metric
Trace of Vectors Space Endomorphism
Transitive Closure of Subset
Trivializing Open Subset and Local Trivialization
Union of Set
Unique Factorization Domain
Units of Ring
Vectors Bundle of Rank $k$
Velocity of $C^{\mathrm{\infty }}$ Curve at Point on $C^{\mathrm{\infty }}$ Manifold with Boundary
Vertex in Simplicial Complex
Vertex of Affine Simplex
Wedge Product
Wedge Sum of Pointed Maps
Wedge Sum of Pointed Sets
Wedge Sum of Pointed Topological Spaces
Well-Ordered Set
hTop Category
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 $C^{\mathrm{\infty }}$ Manifold with Boundary

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References

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