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A Characterization of a Certain Class of Compact Metric Spaces

✍ Scribed by U. Feiste

Publisher: John Wiley and Sons
Year: 1978
Tongue: English
Weight: 226 KB
Volume: 83
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19780830112

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✦ Synopsis

Abstract

Compact metric spaces χ of such a kind, that 𝔹~f~ =𝔹(X), are characterized, 𝔹(X) is the σ‐field of BOREL sets and 𝔹~f~(X) is the field generated by all open subset of X. Our main result is Theorem 5: If χ is a compact metric space, then the following conditions are equivalent:

𝔹~f~(X) =𝔹(X).

card (X) ≦x~0~ and there are k, m__ϵ__N such that card (X^(k)^) = m.

There are k, m__ϵ__N such that χ is homeomorphic to ω^k^ · m + 1.

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