Category:Topology

A

• [×] Algebraic Topology‎ (0)

B

• [×] Baire Spaces‎ (0)
• [×] Boundaries‎ (0)

C

• [×] Clopen Sets‎ (0)
• [+] Closed Sets‎ (2)
• [+] Compact Spaces‎ (16)
• [+] Connectedness‎ (16)
• [+] Continuity‎ (3)
• [+] Countability Axioms‎ (5)
• [×] Covers‎ (0)

D

• [+] Denseness‎ (1)
• [×] Descriptive Set Theory‎ (0)
• [×] Differential Topology‎ (0)

E

• [+] Examples of Topologies‎ (28)

F

• [×] F-Sigma Sets‎ (0)

F cont.

• [×] Filter Theory‎ (0)
• [+] Finite Topological Spaces‎ (1)
• [×] First Category Spaces‎ (0)

G

• [×] G-Delta Sets‎ (0)
• [×] Geometric Topology‎ (0)
• [+] Graph Theory‎ (2)

H

• [×] Homeomorphisms‎ (0)

I

• [×] Isolated Points‎ (0)

K

• [×] Knot Theory‎ (0)

L

• [×] Limit Points‎ (0)

M

• [×] Manifolds‎ (0)
• [+] Metric Spaces‎ (8)
• [×] Metrizable Topologies‎ (0)

N

• [+] Nets (Topology)‎ (1)
• [×] Normed Spaces‎ (0)

O

• [×] Omega-Accumulation Points‎ (0)
• [+] Open Sets‎ (2)

P

• [×] Perfect Sets‎ (0)
• [×] Product Spaces‎ (0)

S

• [×] Second Category Spaces‎ (0)
• [×] Separated Sets‎ (0)
• [+] Separation Axioms‎ (12)
• [×] Set Closures‎ (0)
• [×] Set Exteriors‎ (0)
• [×] Set Interiors‎ (0)

T

• [×] Topological Bases‎ (0)
• [×] Topological Subspaces‎ (0)
• [×] Topological Sum‎ (0)

U

• [+] Uniformities‎ (1)

A

• Arc in Topological Space is Path

B

• Baire Characterisation Theorem
• Banach-Tarski Paradox
• Brouwer's Fixed Point Theorem
• Brouwer's Fixed Point Theorem/General Case

C

• Classification of Compact One-Manifolds
• Classification of Compact Three-Manifolds Supporting Zero-Curvature Geometry
• Classification of Compact Two-Manifolds
• Coarseness Relation on Topologies is Partial Ordering
• Continuity from Union of Restrictions
• Continuity of Composite Mapping
• Continuous Mapping of Partition
• Continuous Mapping on Topological Space Induced by Metric

E

• Empty Set is Element of Topology
• Equidecomposability is an Equivalence Relation
• Equidecomposability Unaffected by Union
• Equidecomposable Nested Sets
• Equidecomposable Subsets
• Existence of Local Coordinates
• Extendability Theorem for Intersection Numbers

F

• Filter on a Product Space Converges iff Projections Converge
• First Subsequence Rule

G

• General Intersection Property of Topological Space
• General Stokes' Theorem
• Generated Topology is a Topology
• Graph of Sine of Reciprocal

H

• H-Cobordism Theorem
• Hausdorff Paradox
• Homology Groups are Groups
• Homotopy Groups are Groups
• Homotopy Groups are Homeomorphism Invariants
• Homotopy is an Equivalence Relation

I

• Inner Limit in Hausdorff Space by Open Neighborhoods
• Inner Limit in Hausdorff Space by Set Closures
• Intersection of Topologies is a Topology

J

• Joining Arcs makes Another Arc
• Joining Paths makes Another Path

L

• Limit Point of Sequence is Accumulation Point

M

• Manipulation of Exterior Derivative
• Metric Induces a Topology

P

• Poincaré Conjecture
• Preimage Theorem
• Projection from Product Topology is Continuous
• Projection from Product Topology is Open
• Pseudometric Induces a Topology

R

• Retraction Theorem
• Rokhlin's Theorem (Intersection Forms)
• Rokhlin's Theorem on Bounded Manifolds and Induced Spin Structures

S

• Sard's Theorem

T

• Topological Completeness is a Topological Property
• Topological Completeness is Weakly Hereditary
• Topological Product of Compact Spaces
• Topology Defined by Closed Sets

U

• Union of Topologies is Not a Topology
• Union of Topologies on Singleton or Doubleton is Topology
• Unit Interval Not Countably Infinite Union of Disjoint Closed Sets

W

• Weak Whitney Immersion Theorem
• Whitney Embedding Theorem