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A Characterization of G. CHOQUET's Pseudo-Topologies

✍ Scribed by Sándor Gacsályi

Publisher
John Wiley and Sons
Year
1968
Tongue
English
Weight
431 KB
Volume
37
Category
Article
ISSN
0025-584X

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✦ Synopsis

This is a direct continuation of the authors paper [4], to which we refer for t,he notions and notations employed. (See also [I, 21 and [3].) I n § 6 of [4] we have shown that every pseudo-topology in the sense of G. CHOQUET can be considered as a limiting, and hence also as a t-maximal filter of perfect topogenous orders. (Cf. [4], Theorem 3.) Once it is known that every pseudotopology can be regarded as a t-maximal filter of perfect topogenous orders, it is natural to ask for the condition which must be imposed upon a tmaximal filter in order that it may yield a pseudo-topology. This question was left open in [4], and it is the aim of the present note to supply an answer, i.e. to give a characterization of pseudo-topologies in terms of Tmaximal filters of perfect topogenous orders.

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