Pseudonormal space
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:
- Every normal space is pseudonormal.
- Every pseudonormal space is regular.
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
- ↑ 1.0 1.1 Nyikos, Peter J. (2001), "A history of the normal Moore space problem", Handbook of the History of General Topology, Hist. Topol. 3, Dordrecht: Kluwer Academic Publishers, pp. 1179–1212, MR 1900271
- ↑ 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.