منابع مشابه
On Radon measures on first-countable spaces
It is shown that every Radon measure on a first-countable Hausdorff space is separable provided ω1 is a precaliber of every measurable algebra. As the latter is implied by MA(ω1), the result answers a problem due to D. H. Fremlin. Answering the problem posed by D. H. Fremlin ([4], 32R(c)), we show in this note that, assuming (∗) ω1 is a precaliber of every measurable Boolean algebra, every Rado...
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The minimum weight of a nowhere first-countable compact space of countable π-weight is shown to be κB, the least cardinal κ for which the real line R can be covered by κ many nowhere dense sets.
متن کاملCH and first countable , countably compact spaces ✩
We show that it is consistent with the Continuum Hypothesis that first countable, countably compact spaces with no uncountable free sequences are compact. As a consequence, we get that CH does not imply the existence of a perfectly normal, countably compact, non-compact space, answering a question of Nyikos (Question 287 in the numbering of van Mill and Reed, Open Problems in Topology, Elsevier...
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Improving a result from the paper “Spaces in countable web” by Yoshikazu Yasui and Zhi-min Gao we show that Tychonoff spaces in countable discrete web may contain closed discrete subsets of arbitrarily big cardinality.
متن کاملFirst Countable, Countably Compact Spaces and the Continuum Hypothesis
We build a model of ZFC+CH in which every first countable, countably compact space is either compact or contains a homeomorphic copy of ω1 with the order topology. The majority of the paper consists of developing forcing technology that allows us to conclude that our iteration adds no reals. Our results generalize Saharon Shelah’s iteration theorems appearing in Chapters V and VIII of Proper an...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1976
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1976.65.113