A first countable linearly Lindelöf not Lindelöf topological space
نویسندگان
چکیده
منابع مشابه
Some results on linearly Lindelöf spaces ∗
Some new results about linearly Lindelöf spaces are given here. It is proved that if X is a space of countable spread and X = Y ∪ Z, where Y and Z are meta-Lindelöf spaces, then X is linearly Lindelöf. Moreover, we give a positive answer to a problem raised by A.V. Arhangel’skii and R.Z. Buzyakova.
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There is a locally compact Hausdorff space of weight אω which is linearly Lindelöf and not Lindelöf.
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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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A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...
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We study conditions on a topological space that guarantee that its product with every Lindelöf space is Lindelöf. The main tool is a condition discovered by K. Alster and we call spaces satisfying his condition Alster spaces. We also study some variations on scattered spaces that are relevant for this question.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2011
ISSN: 0166-8641
DOI: 10.1016/j.topol.2011.06.057