Category:Properties of topological spaces
This category lists important properties of topological spaces. By a property of topological spaces, we mean something that every topological space either satisfies, or does not satisfy. Properties of topological spaces are invariant under performing homeomorphisms. In other words, if two topological spaces are homeomorphic, then one has a given property iff the other one has.
Subcategories
This category has the following 14 subcategories, out of 14 total.
H
P
S
V
Pages in category "Properties of topological spaces"
The following 199 pages are in this category, out of 199 total.
A
C
- Cantor space
- Cech-complete space
- Closed sub-Euclidean space
- Collectionwise Hausdorff space
- Collectionwise normal space
- Compact Hausdorff space
- Compact manifold
- Compact metrizable space
- Compact simply connected manifold
- Compact space
- Compact T1 space
- Compactly generated Hausdorff space
- Compactly generated space
- Compactly homogeneous space
- Compactly nondegenerate space
- Completely metrizable space
- Completely regular space
- Connected Hausdorff space
- Connected manifold
- Connected normal space
- Connected regular space
- Connected space
- Connected T1 space
- Continuum
- Contractible manifold
- Contractible space
- Countable chain condition
- Countably compact space
- Countably orthocompact space
- Cozero-complemented space
- CW-space
D
F
H
- H-closed space
- H-space
- Hausdorff space
- Hemicompact space
- Hereditarily collectionwise normal space
- Hereditarily compact space
- Hereditarily irresolvable space
- Hereditarily normal Hausdorff space
- Hereditarily normal space
- Hereditarily paracompact space
- Hereditarily separable space
- Homogeneous space
- Homology manifold
- Homotopy-CW-space
- Homotopy-minimal manifold
- Hurewicz space
L
- Limit point-compact space
- Lindelof space
- Linearly orderable space
- Linearly stratifiable space
- Locally compact Hausdorff space
- Locally compact paracompact Hausdorff space
- Locally compact space
- Locally connected space
- Locally contractible space
- Locally Euclidean space
- Locally Hausdorff space
- Locally metrizable space
- Locally normal space
- Locally path-connected space
- Locally regular space
- Locally simply connected space
- Luzin space
M
N
P
R
S
- SDR-contractible space
- Second-countable space
- Second-countable T1 space
- Self-based space
- Semilocally 1-connected space
- Semilocally simply connected space
- Semiregular space
- Semistratifiable space
- Separable space
- Sequential space
- Sequentially compact space
- SI-space
- Sigma-compact space
- Simple space
- Simply connected manifold
- Simply connected space
- Snake-like space
- Sober space
- Sober T0 space
- Sober T1 space
- Space with abelian fundamental group
- Space with Abelian mapping class group
- Space with Euler characteristic one
- Space with Euler characteristic zero
- Space with finitely generated homology
- Space with finitely generated homotopy groups
- Space with free homology
- Space with homology of finite type
- Space with perfect fundamental group
- Space with torsion-free homology
- Space with trivial mapping class group
- Stratifiable space
- Strongly locally compact space
- Strongly paracompact space
- Strongly screenable space
- Sub-Euclidean space
- Submaximal space
- Submetrizable space
- Subparacompact space
- Suddenly contractible space
- Supercompact space
- Symmetric space