index of properties of topological spaces

Topological axioms

• topological structures on sets

• continuous maps

• categories, functors and natural transformations

Compactness Properties

• compact

• countably compact

• Lindelöf (http://planetmath.org/Lindelof), finally compact (http://planetmath.org/Lindelof)

• locally compact

• metacompact

• paracompact

• strongly locally compact

• sequentially compact

• $\sigma$-compact (http://planetmath.org/SigmaCompact)

• $\sigma$-locally compact

• weakly countably compact (http://planetmath.org/LimitPointCompact), limit point compact

Countability Properties

• first countable (http://planetmath.org/FirstCountable)

• second countable (http://planetmath.org/SecondCountable)

• separable

Connectedness Properties

• biconnected

• arc connected

• connected (http://planetmath.org/ConnectedSpace)

• connected im kleinen

• extremally disconnected

• hyperconnected

• locally arc connected

• locally connected

• locally path connected

• path-connected

• punctiform

• scattered

• totally disconnected

• totally path disconnected

• totally separated

• ultraconnected

Contractibility Proprties

• absolute retract

• absolute neighborhood retract

• contractible to a point

• locally simply connected

• semi-locally simply connected

• simply connected

• locally homeomorphic and covering spaces

• fibrations

• homotopy groups

• homotopy as a functor

• homotopy type

• lifting properties of fibrations

Separation Properties (http://planetmath.org/SeparationAxioms)

• completely normal

• completely regular, Tychonoff

• fully normal

• fully $T_4$ (http://planetmath.org/FullyT4)

• normal

• perfectly $T_4$

• perfectly normal

• regular

• semiregular

• $T_0$ (http://planetmath.org/T0Space), Kolmogorov (http://planetmath.org/T0Space)

• $T_1$ (http://planetmath.org/T1Space), Fréchet (http://planetmath.org/T1Space)

• $T_2$ (http://planetmath.org/T2Space), Hausdorff (http://planetmath.org/T2Space)

• $T_{2⁤\frac{1}{2}}$ (http://planetmath.org/CompletelyHaussdorff), completely Hausdorff

• $T_3$ (http://planetmath.org/SeparationAxioms)

• $T_{3⁤\frac{1}{2}}$ (http://planetmath.org/SeparationAxioms)

• $T_4$ (http://planetmath.org/SeparationAxioms)

• $T_5$ (http://planetmath.org/SeparationAxioms)

• Urysohn, functionally Hausdorff

Subset Properties

• open

• closed

• clopen

• regular open

• regular closed (http://planetmath.org/RegularOpenSet)

• locally closed

• dense

• nowhere dense

• meager

• residual

• separated sets (http://planetmath.org/Separated)

• completely separated sets (http://planetmath.org/CompletelySeparated)

Topological groups

• full subgroup

Homology

Title	index of properties of topological spaces
Canonical name	IndexOfPropertiesOfTopologicalSpaces
Date of creation	2013-03-22 14:39:29
Last modified on	2013-03-22 14:39:29
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	29
Author	rspuzio (6075)
Entry type	Topic
Classification	msc 54-00