A separable normal topological group need not be Lindelöf
نویسندگان
چکیده
منابع مشابه
A SEPARABLE NORMAL TOPOLOGICAL GROUP WHICH IS NOT LINDELijF
In 1968 Wilansky asked whether a separable normal topological group must be Lindelof. In [7] this question was answered in the negative, assuming CH, by constructing a hereditarily separable, normal group which is not Lindeliif. We give an example of a separable normal group which contains a closed subspace homeomorphic to an uncountable regular cardinal, in ZFC only. Of course we have to sacri...
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Theorem 1 proves (among the others) that for a locally compact topological group X the following assertions are equivalent: (i) X is metrizable and s-compact. (ii) CpðXÞ is analytic. (iii) CpðXÞ is K-analytic. (iv) CpðXÞ is Lindelöf. (v) CcðX Þ is a separable metrizable and complete locally convex space. (vi) CcðX Þ is compactly dominated by irrationals. This result supplements earlier results ...
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ژورنال
عنوان ژورنال: General Topology and its Applications
سال: 1976
ISSN: 0016-660X
DOI: 10.1016/0016-660x(76)90033-7