# index of properties of topological spaces

Topological axioms

• topological structures on sets

Compactness Properties

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

• strongly locally compact

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

• $\sigma$-locally compact

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

Countability Properties

Connectedness Properties

• biconnected

• arc connected

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

• locally arc connected

• locally path connected

• punctiform

• totally path disconnected

• totally separated

Contractibility Proprties

• absolute neighborhood retract

• contractible to a point

http://planetmath.org/SeparationAxioms)

• completely regular, Tychonoff

• fully $T_{4}$ (http://planetmath.org/FullyT4)

• normal

• perfectly $T_{4}$

• perfectly normal

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

• dense

• nowhere dense

• meager

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

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

Title index of properties of topological spaces IndexOfPropertiesOfTopologicalSpaces 2013-03-22 14:39:29 2013-03-22 14:39:29 rspuzio (6075) rspuzio (6075) 29 rspuzio (6075) Topic msc 54-00