Space (mathematics)

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History

Euclid Analytic geometry René Descartes Equivalence relations Congruence

28 related topics

Types of spaces

Algebraic Field Real numbers Complex number Complex plane

112 related topics

Taxonomy of spaces

Mathematical logic Homeomorphism Category theory Forgetful Functor

13 related topics

Spaces and structure

Fundamental group Spectrum of a ring Finitely many principal base sets and finitely many auxiliary base sets Transport of structure Modules

13 related topics

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Overview

Mathematics
Set Set (mathematics)
Universe Universe (mathematics)
Mathematical structure
Elements Element (mathematics)
Subset
Euclidean spaces Euclidean space
Linear spaces Linear space
Topological spaces Topological space
Hilbert spaces Hilbert space
Probability spaces Probability space
Mathematical objects Mathematical object
Points Point (mathematics)
Isomorphism
"Types of spaces" Space (mathematics)
Geometric "space" Geometric space
Algebraic "structure" Algebraic structure
Bourbaki Nicolas Bourbaki

History

Euclid
Analytic geometry
René Descartes
Equivalence relations Equivalence relation
Congruence Congruence (geometry)
Similarity Similarity (geometry)
Homotheties Homothetic transformation
Gaspard Monge
Projective geometry
Hyperbolic geometry
Nikolai Lobachevsky
János Bolyai
Carl Friedrich Gauss
Eugenio Beltrami
Felix Klein
Non-Euclidean geometry
"Erlangen programme" Erlangen program
Hilbert's axioms
Tarski's axioms
Birkhoff's axioms
Primitive notions Primitive notion
Axioms Axiom
Dedekind cuts Dedekind cut
Projective space
Bernhard Riemann
Functions Function (mathematics)
Function spaces Function space
Functional analysis

Taxonomy of spaces

Mathematical logic
Homeomorphism
Category theory
Forgetful Forgetful functor
Functor
Classes Class (set theory)
Self-homeomorphism
Injective Injective function
Surjective Surjective function
Bijective Bijection
Inverse Inverse function
Commutative Commutative diagram
Fine topology Fine topology (potential theory)

Types of spaces

Algebraic Algebra
Field Field (mathematics)
Real numbers Real number
Complex number
Complex plane
Field extensions Examples of vector spaces
Linearly independent Linear independence
Mathematical analysis
Open sets Open set
Continuous functions Continuous function
Convergent sequences, limits Limit of a sequence
Uniform continuity
Bounded sets Bounded set
Cauchy sequences Cauchy sequence
Differentiable functions Differentiable function
Open interval
Real line
Closed interval
Inductive dimension
Lebesgue covering dimension
General topology
Compact topological spaces Compact space
Extended real line
Manifolds Manifold (geometry)
Linear topological space Topological vector space
Affine Affine space
John Baez John C. Baez
Metric space
Metrizable
Complete Complete metric space

Spaces and structure

Fundamental group
Spectrum of a ring
Finitely many principal base sets and finitely many auxiliary base sets Equivalent definitions of mathematical structures
Transport of structure
Modules Module (mathematics)
Rings Ring (mathematics)
Module appears to be a linear space Vector space
Algebraic closure
Analysis Complex analysis
A striking feature of projective planes is the symmetry of the roles played by points and lines Duality (projective geometry)
Formalized via two base sets Graph (discrete mathematics)
Mereotopology
Point-free geometry Whitehead's point-free geometry

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Map overview Semantic statistics

Nodes190

Edges189

Triples8

Avg. degree1.99

Density0.010526

Components1

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