Browse By

All Topology

Proved results about the properties a space keeps under continuous deformation. Belongs here: topological theorems. Does not belong here: results still conjectural, and results that turn on exact distance or curvature rather than continuous deformation, which belong under Geometry instead.

Facts

Comparison

Era Of Emergence

1895 1

All Topology

48 entries

Branch

Topic Area

Proved

Proved By

Named After

Statement Form

Alexander Duality

Alexander's Theorem, Braid Closure

Atiyah-Singer Index Theorem

Borsuk-Ulam Theorem

Brouwer Fixed-Point Theorem

Brown Representability Theorem

Cantor's Intersection Theorem

Classification of Surfaces

Curtis-Hedlund-Lyndon Theorem

De Rham's Theorem

Donaldson's Theorem

Eilenberg-Zilber Theorem

Four Color Theorem

Freedman's Theorem

Freudenthal Suspension Theorem

Gromov's Non-Squeezing Theorem

Hairy Ball Theorem

H-Cobordism Theorem

Hurewicz Theorem

Invariance of Domain

Jordan Curve Theorem

Kakutani Fixed-Point Theorem

Kuiper's Theorem

Kunneth Theorem

Lefschetz Fixed-Point Theorem

Leray-Hirsch Theorem

Leray-Schauder Fixed-Point Theorem

Mayer-Vietoris Theorem

Nagata-Smirnov Metrization Theorem

Poincare Conjecture

Poincare Duality Theorem

Poincare Lemma

Poincare-Hopf Theorem

Reidemeister's Theorem

Sard's Theorem

Schoenflies Theorem

Smale's Theorem (Sphere Eversion)

Thurston's Geometrization Theorem

Tietze Extension Theorem

Tychonoff's Theorem

Uniformization Theorem

Universal Coefficient Theorem

Urysohn Metrization Theorem

Urysohn's Lemma

Van Kampen's Theorem

Whitehead Theorem

Whitney Embedding Theorem

Whitney Immersion Theorem