In mathematics, in the realm of topology, a paranormal space (Nyikos 1984) is a topological space in which every countable discrete collection of closed sets has a locally finite open expansion.
| Separation axioms in topological spaces | |
|---|---|
| Kolmogorov classification | |
| T0 | (Kolmogorov) |
| T1 | (Fréchet) |
| T2 | (Hausdorff) |
| T2½ | (Urysohn) |
| completely T2 | (completely Hausdorff) |
| T3 | (regular Hausdorff) |
| T3½ | (Tychonoff) |
| T4 | (normal Hausdorff) |
| T5 | (completely normal Hausdorff) |
| T6 | (perfectly normal Hausdorff) |
See also
edit- Collectionwise normal space – Property of topological spaces stronger than normality
- Locally normal space
- Monotonically normal space – Property of topological spaces stronger than normality
- Normal space – Type of topological space – a topological space in which every two disjoint closed sets have disjoint open neighborhoods
- Paracompact space – Topological space in which every open cover has an open refinement that is locally finite – a topological space in which every open cover admits an open locally finite refinement
- Separation axiom – Axioms in topology defining notions of "separation"
References
edit- Nyikos (1984), "Problem Section: Problem B. 25", Top. Proc., 9
- Smith, Kerry D.; Szeptycki, Paul J. (2000), "Paranormal spaces under ◊*", Proceedings of the American Mathematical Society, 128 (3): 903–908, doi:10.1090/S0002-9939-99-05032-7, ISSN 0002-9939, MR 1622981
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