Paracompactness and product spaces
نویسندگان
چکیده
منابع مشابه
Paracompactness and Product Spaces
A topological space is called paracompact (see [2 J) if (i) it is a Hausdorff space (satisfying the T2 axiom of [l]), and (ii) every open covering of it can be refined by one which is "locally finite" ( = neighbourhood-finite; that is, every point of the space has a neighbourhood meeting only a finite number of sets of the refining covering). J. Dieudonné has proved [2, Theorem 4] that every se...
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In this article, we present the concept of supra paracompact spaces and study its basic properties. We elucidate its relationship with supra compact spaces and prove that the property of being a supra paracompact space is weakly hereditary and topological properties. Also, we provide some examples to show some results concerning paracompactness on topology are invalid on supra topology. Finally...
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The axiom of multiple choice implies that metric spaces are paracompact but the reverse implication cannot be proved in set theory without the axiom of choice. 1. Background, Definitions and Summary of Results. Working in set theory without the axiom of choice we study the deductive strength of the assertion MP: Metric spaces are paracompact. (Definitions are given below.) MP was first proved i...
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a) X is strongly paracompact; b) X is paracompact; c) X is metacompact; d) X is weakly θ-refinable; e) Every open cover of X has a point-countable open refinement; f) X is subparacompact; g) If C is a closed subspace of X, then there are discrete closed sets S and T which are, respectively, well-ordered and reverse-well-ordered by the given ordering of X, have S ∪ T ⊂ C, and have the property t...
متن کاملOn the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces
We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space which does not include a perfect pre-image of ω1 is hereditarily paracompact. This is the fifth in a series of papers ([LTo], [L2], [FTT], [LT], [T1] being the logically previous ones) that establish powerful topological consequences in models ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1948
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1948-09118-2