Paranormal space

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)

* History

Not to be confused with paranormal phenomena outside the range of normal experience.

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.

## See also

* 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

* 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

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