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index of properties of topological spaces
The puropse of this meta-entry is to list all topological properties discussed in this encyclopaedia (or soon to be added). The properties have been classified into several broad categories; within each category, they have been listed alphabetically. For consistency, the adjectival forms of terms have been used whenever possible. When more than one term appears on a single line, this signifies that the terms are synonyms. For further information on any topic, please click on the appropriate link.
Topological axioms
- topological structures on sets
- continuous maps
- categories, functors and natural transformations
Compactness Properties
- compact
- countably compact
- Lindelöf, finally compact
- locally compact
- metacompact
- paracompact
- strongly locally compact
- sequentially compact
- $\sigma$ -compact
- $\sigma$ -locally compact
- weakly countably compact, limit point compact
Countability Properties
- first countable
- second countable
- separable
Connectedness Properties
- biconnected
- arc connected
- connected
- 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
- absolute retract
- absolute neighborhood retract
- contractible to a point
Homotopic properties
- 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
- completely normal
- completely regular, Tychonoff
- fully normal
- fully $T_4$
- normal
- perfectly $T_4$
- perfectly normal
- regular
- semiregular
- $T_0$ , Kolmogorov
- $T_1$ , Fréchet
- $T_2$ , Hausdorff
- $T_{2 \frac12}$ , completely Hausdorff
- $T_3$
- $T_{3 \frac12}$
- $T_4$
- $T_5$
- Urysohn, functionally Hausdorff
Subset Properties
- open
- closed
- clopen
- regular open
- regular closed
- locally closed
- dense
- nowhere dense
- meager
- residual
- separated sets
- completely separated sets
Topological groups
- full subgroup
Homology
index of properties of topological spaces is owned by Raymond Puzio, matte, yark, Juan M. Marquez B., Thomas Foregger, Rui Palma, bci1.
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