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[edit]
- ^ 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
- ^ 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.
Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
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