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Statistical metric spaces as related to topological spaces

✍ Scribed by B. Morrel; J. Nagata

Publisher
Elsevier Science
Year
1978
Weight
536 KB
Volume
9
Category
Article
ISSN
0016-660X

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✦ Synopsis

Our discussion answers the question? as to what topological spaces arc: statistcaily metrizable in the sense of Schweizer and Sklar [5] and whether this can be discerned by the t-norm Ian the space in the Menger triangle relaiion. Namely we prove (1) the class gf topological Menger q'aces coincides with that of semi-metrizable topological spaces, and (2) no condition weaker than I= ~p,<~ T(x, x) can guarantee that a Menger space satisIfying the IL4enger triangle relation under T is topological.

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## Abstract The coGalois group associated to a torsion free cover of a ℀‐module are known to have a canonical topology. In this paper we will see that this topology can be deduced by __p^k^__‐roots of elements of coGalois groups over β„€~__p__~ (__p__ is a prime). We shall investigate in the metric a