# Category:Definition Equivalences

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See also: Help:Multiple Definitions

## Subcategories

This category has the following 9 subcategories, out of 9 total.

### E

### G

## Pages in category "Definition Equivalences"

The following 200 pages are in this category, out of 322 total.

(previous page) (next page)### A

- Equivalence of Definitions of Abelian Group
- Equivalence of Definitions of Absolute Convergence of Product
- Equivalence of Definitions of Absolute Convergence of Product of Complex Numbers
- Equivalence of Definitions of Absolute Value Function
- Equivalence of Definitions of Adherent Point
- Equivalence of Definitions of Affine Space
- Equivalence of Definitions of Algebra of Sets
- Equivalence of Definitions of Algebraically Closed Field
- Equivalence of Definitions of Almost Perfect Number
- Equivalence of Definitions of Amicable Pair
- Equivalence of Definitions of Amicable Triplet
- Equivalence of Definitions of Analytic Basis
- Equivalence of Definitions of Analytic Function
- Equivalence of Definitions of Antisymmetric Relation
- Equivalence of Definitions of Arborescence
- Equivalence of Definitions of Associate in Integral Domain
- Equivalence of Definitions of Associate in Integral Domain/Definition 1 Equivalent to Definition 2
- Equivalence of Definitions of Associate in Integral Domain/Definition 1 Equivalent to Definition 3
- Equivalence of Definitions of Asymmetric Relation
- Equivalence of Definitions of Asymptotically Equal Sequences

### B

- Equivalence of Definitions of Baire Space
- Equivalence of Definitions of Basis of Vector Space
- Equivalence of Definitions of Bernoulli Numbers
- Equivalence of Definitions of Beta Function
- Equivalence of Definitions of Bijection
- Equivalence of Definitions of Bijection/Definition 1 iff Definition 2
- Equivalence of Definitions of Bijection/Definition 1 iff Definition 3
- Equivalence of Definitions of Bijection/Definition 1 iff Definition 4
- Equivalence of Definitions of Bijection/Definition 3 iff Definition 4
- Equivalence of Definitions of Bijection/Definition 3 iff Definition 5
- Equivalence of Definitions of Binomial Coefficient
- Equivalence of Definitions of Boolean Algebra
- Equivalence of Definitions of Bottom
- Equivalence of Definitions of Bounded Lattice
- Equivalence of Definitions of Bounded Metric Space
- Equivalence of Definitions of Bounded Real-Valued Function
- Equivalence of Definitions of Bounded Subset of Real Numbers

### C

- Equivalence of Definitions of Cantor Set
- Equivalence of Definitions of Ceiling Function
- Equivalence of Definitions of Change of Basis Matrix
- Equivalence of Definitions of Characteristic of Ring
- Equivalence of Definitions of Closed Element
- Equivalence of Definitions of Closed Linear Span
- Equivalence of Definitions of Closed Set in Metric Space
- Equivalence of Definitions of Closed Set
- Equivalence of Definitions of Closure of Topological Subspace
- Equivalence of Definitions of Closure Operator
- Alexander's Compactness Theorem
- Compact Space satisfies Finite Intersection Axiom
- Equivalence of Definitions of Compact Topological Space
- Equivalence of Definitions of Compact Topological Subspace
- Equivalence of Definitions of Compatible Atlases
- Equivalence of Definitions of Complement of Subgroup
- Equivalence of Definitions of Complete Metric Space
- Equivalence of Definitions of Complex Cross Product
- Equivalence of Definitions of Complex Dot Product
- Equivalence of Definitions of Complex Exponential Function
- Equivalence of Definitions of Complex Exponential Function/Sum of Series equivalent to Definition by Real Functions
- Equivalence of Definitions of Complex Exponential Function/Sum of Series equivalent to Differential Equation
- Equivalence of Definitions of Complex Exponential Function/Sum of Series equivalent to Limit of Sequence
- Equivalence of Definitions of Complex Inverse Cosecant Function
- Equivalence of Definitions of Complex Inverse Cosine Function
- Equivalence of Definitions of Complex Inverse Cotangent Function
- Equivalence of Definitions of Complex Inverse Hyperbolic Cosecant
- Equivalence of Definitions of Complex Inverse Hyperbolic Cosine
- Equivalence of Definitions of Complex Inverse Hyperbolic Cotangent
- Equivalence of Definitions of Complex Inverse Hyperbolic Secant
- Equivalence of Definitions of Complex Inverse Hyperbolic Sine
- Equivalence of Definitions of Complex Inverse Hyperbolic Tangent
- Equivalence of Definitions of Complex Inverse Secant Function
- Equivalence of Definitions of Complex Inverse Sine Function
- Equivalence of Definitions of Complex Inverse Tangent Function
- Equivalence of Definitions of Complex Natural Logarithm
- Equivalence of Definitions of Complex Number
- Equivalence of Definitions of Component
- Equivalence of Definitions of Composition of Mappings
- Equivalence of Definitions of Concave Real Function
- Equivalence of Definitions of Congruence
- Equivalence of Definitions of Integer Congruence
- Equivalence of Definitions of Conic Section
- Equivalence of Definitions of Conjugate of Group Element
- Equivalence of Definitions of Connected Set (Complex Analysis)
- Equivalence of Definitions of Connected Set
- Equivalence of Definitions of Connected Topological Space
- Equivalence of Definitions of Connected Topological Space/No Separation iff No Union of Closed Sets
- Equivalence of Definitions of Consistent Proof System
- Equivalence of Definitions of Consistent Set of Formulas
- Equivalence of Definitions of Constant Polynomial
- Equivalence of Definitions of Metric Space Continuity at Point
- Equivalence of Definitions of Continuous Mapping between Topological Spaces/Point
- Equivalence of Definitions of Continuous Mapping between Topological Spaces
- Equivalence of Definitions of Continuity on Metric Spaces
- Equivalence of Definitions of Contractible Space
- Equivalence of Definitions of Convergent Complex Sequence
- Equivalence of Definitions of Convergent of Continued Fraction
- Equivalence of Definitions of Convergent Sequence in Metric Space
- Equivalence of Definitions of Convergent Sequence in Metric Space/Definition 1 iff Definition 2
- Equivalence of Definitions of Convergent Sequence in Metric Space/Definition 1 iff Definition 3
- Equivalence of Definitions of Convergence in Normed Division Rings
- Equivalence of Definitions of Convex Real Function
- Equivalence of Definitions of Convex Set (Order Theory)
- Equivalence of Definitions of Coreflexive Relation
- Equivalence of Definitions of Cosecant of Angle
- Equivalence of Definitions of Cosine of Angle
- Equivalence of Definitions of Cotangent of Angle
- Equivalence of Definitions of Countable Set
- Countably Compact Space satisfies Countable Finite Intersection Axiom
- Equivalence of Definitions of Countably Compact Space
- Equivalence of Definitions of Countably Infinite Set
- Equivalence of Definitions of Curvature
- Equivalence of Definitions of Cyclic Group

### D

- Equivalence of Definitions of Dedekind Domain
- Equivalence of Definitions of Derivative
- Equivalence of Definitions of Differentiable Real Function at Point
- Equivalence of Definitions of Direct Limit of Sequence of Groups
- Equivalence of Definitions of Distributive Lattice
- Equivalence of Definitions of Division Ring
- Equivalence of Definitions of Dominate (Set Theory)
- Equivalence of Definitions of Dot Product
- Equivalence of Definitions of Dual Relation

### E

- Equivalence of Definitions of Empty Set
- Equivalence of Definitions of Exponential Function
- Equivalence of Definitions of Logical Consistence
- Equivalence of Definitions of Norm of Linear Functional
- Equivalence of Definitions of Norm of Linear Functional/Corollary
- Equivalence of Definitions of Null Set in Euclidean Space
- Equivalence of Definitions of Sine and Cosine
- Equivalence of Definitions of Equivalence Relation
- Equivalence of Definitions of Equivalent Division Ring Norms
- Equivalence of Definitions of Euler Lucky Number
- Equivalence of Definitions of Euler's Number
- Equivalence of Definitions of Euler's Number/Proof 1
- Equivalence of Definitions of Euler's Number/Proof 2
- Equivalence of Definitions of Even Integer
- Equivalence of Definitions of Continuous Mapping between Topological Spaces/Everywhere
- Equivalence of Definitions of Exterior
- Equivalence of Definitions of Exterior Point (Complex Analysis)
- Equivalence of Definitions of Extremally Disconnected Space
- Extremally Disconnected by Disjoint Open Sets
- Extremally Disconnected by Interior of Closed Sets

### F

### G

- Equivalence of Definitions of Gamma Function
- Equivalence of Definitions of Generalized Ordered Space
- Equivalence of Definitions of Generalized Pentagonal Number
- Equivalence of Definitions of Generated Subgroup
- Equivalence of Definitions of Generated Submodule
- Equivalence of Definitions of Golden Mean
- Equivalence of Definitions of Greatest Common Divisor

### H

- Equivalence of Definitions of Heptagonal Number
- Equivalence of Definitions of Hereditarily Compact
- Equivalence of Definitions of Hexagonal Number
- Equivalence of Definitions of Homeomorphic Metric Spaces
- Equivalence of Definitions of Homeomorphic Topological Spaces
- Equivalence of Definitions of Hyperbola
- Equivalence of Definitions of Hyperbolic Cosecant
- Equivalence of Definitions of Hyperbolic Cotangent
- Equivalence of Definitions of Hyperbolic Secant
- Equivalence of Definitions of Hyperbolic Tangent

### I

- Equivalence of Definitions of Image of Mapping
- Equivalence of Definitions of Independent Events
- Equivalence of Definitions of Independent Subgroups
- Equivalence of Definitions of Infimum of Real-Valued Function
- Equivalence of Definitions of Infinite Cyclic Group
- Equivalence of Definitions of Infinite Order Element
- Equivalence of Definitions of Initial Topology
- Equivalence of Definitions of Injection
- Equivalence of Definitions of Integral Domain
- Equivalence of Definitions of Integral Element of Algebra
- Equivalence of Definitions of Interior (Topology)
- Equivalence of Definitions of Inverse Image Mapping of Mapping
- Equivalence of Definitions of Inverse Image Mapping of Relation
- Equivalence of Definitions of Inverse Mapping
- Equivalence of Definitions of Involutive Mapping
- Equivalence of Definitions of Irreducible Element of Ring
- Equivalence of Definitions of Irreducible Polynomial over Field
- Equivalence of Definitions of Irreducible Space
- Equivalence of Definitions of Irreducible Space/3 iff 6
- Equivalence of Definitions of Irreducible Space/3 iff 7
- Equivalence of Definitions of Isolated Point
- Equivalence of Definitions of Isometry of Metric Spaces

### L

- Equivalence of Definitions of Lattice
- Equivalence of Definitions of Legendre Symbol
- Equivalence of Definitions of Limit Inferior of Sequence of Sets
- Equivalence of Definitions of Limit of Function in Metric Space
- Equivalence of Definitions of Limit Point
- Equivalence of Definitions of Limit Superior of Sequence of Sets
- Equivalence of Definitions of Lipschitz Equivalent Metrics
- Equivalence of Definitions of Local Basis
- Equivalence of Definitions of Local Ring Homomorphism
- Equivalence of Definitions of Locally Compact Hausdorff Space
- Equivalence of Definitions of Locally Connected Space
- Equivalence of Definitions of Locally Path-Connected Space
- Equivalence of Definitions of Lower Set
- Equivalence of Definitions of Lucas Numbers