Jump to content

Topological space

From Wikiquote

In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.

Quotes

[edit]
  • For a normal topological space, there exist three different approaches to define its dimension, due to Lebesgue and Čech (covering dimension dim), Urysohn and Menger (small inductive dimension ind), and Poincaré, Brouwer, and Čech (large inductive dimension Ind). All the three dimensions coincide for separable metric spaces (Tumarkin-Urysohn–Hurewitz's theorem proved in the late 20s), the equality dim X = Ind X holds for any metric space X (Katetov–Morita's theorem, 1954), while in 1962, Roy [Roy] constructed his famous example of a complete metric space Y such that ind Y = 0, but dim Y = Ind Y = 1.
[edit]
Wikipedia
Wikipedia
Wikipedia has an article about:



Mathematics
Mathematicians
(by country)

AbelAnaxagorasArchimedesAristarchus of SamosAverroesArnoldBanachCantorCartanChernCohenDescartesDiophantusErdősEuclidEulerFourierGaussGödelGrassmannGrothendieckHamiltonHilbertHypatiaLagrangeLaplaceLeibnizMilnorNewtonvon NeumannNoetherPenrosePerelmanPoincaréPólyaPythagorasRiemannRussellSchwartzSerreTaoTarskiThalesTuringWeilWeylWilesWitten

Numbers

123360eπFibonacci numbersIrrational numberNegative numberNumberPrime numberQuaternionOctonion

Concepts

AbstractionAlgorithmsAxiomatic systemCompletenessDeductive reasoningDifferential equationDimensionEllipseElliptic curveExponential growthInfinityIntegrationGeodesicInductionProofPartial differential equationPrinciple of least actionPrisoner's dilemmaProbabilityRandomnessTheoremTopological spaceWave equation

Results

Euler's identityFermat's Last Theorem

Pure math

Abstract algebraAlgebraAnalysisAlgebraic geometry (Sheaf theory) • Algebraic topologyArithmeticCalculusCategory theoryCombinatoricsCommutative algebraComplex analysisDifferential calculusDifferential geometryDifferential topologyErgodic theoryFoundations of mathematicsFunctional analysisGame theoryGeometryGlobal analysisGraph theoryGroup theoryHarmonic analysisHomological algebraInvariant theoryLogicNon-Euclidean geometryNonstandard analysisNumber theoryNumerical analysisOperations researchRepresentation theoryRing theorySet theorySheaf theoryStatisticsSymplectic geometryTopology

Applied math

Computational fluid dynamicsEconometricsFluid mechanicsMathematical physicsScience

History of math

Ancient Greek mathematicsEuclid's ElementsHistory of algebraHistory of calculusHistory of logarithmsIndian mathematicsPrincipia Mathematica

Other

Mathematics and mysticismMathematics educationMathematics, from the points of view of the Mathematician and of the PhysicistPhilosophy of mathematicsUnification in science and mathematics