Approximating Radon measures on first-countable compact spaces
نویسندگان
چکیده
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 کاملNonseparable Radon measures and small compact spaces
We investigate the problem if every compact space K carrying a Radon measure of Maharam type κ can be continuously mapped onto the Tikhonov cube [0, 1] (κ being an uncountable cardinal). We show that for κ ≥ cf(κ) ≥ ω2 this holds if and only if κ is a precaliber of measure algebras. Assuming that there is a family of ω1 null sets in 21 such that every perfect set meets one of them, we construct...
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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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If Martin’s Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable L1 space, then there is a continuous surjection from X onto [0, 1]1 .
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2000
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-86-1-15-23