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, MR 1622981