Jump to content

Pseudonormal space

From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by OAbot (talk | contribs) at 02:47, 17 April 2020 (Open access bot: doi added to citation with #oabot.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In mathematics, in the field of topology, a topological space is said to be pseudonormal if given two disjoint closed sets in it, one of which is countable, there are disjoint open sets containing them.[1] Note the following:

An example of a pseudonormal Moore space that is not metrizable was given by F. B. Jones (1937), in connection with the conjecture that all normal Moore spaces are metrizable.[1][2]

References

  1. ^ a b Nyikos, Peter J. (2001), "A history of the normal Moore space problem", Handbook of the History of General Topology, Hist. Topol., vol. 3, Dordrecht: Kluwer Academic Publishers, pp. 1179–1212, MR 1900271
  2. ^ Jones, F. B. (1937), "Concerning normal and completely normal spaces", Bulletin of the American Mathematical Society, 43 (10): 671–677, doi:10.1090/S0002-9904-1937-06622-5, MR 1563615.