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...
متن کاملParacompactness and an Example Due To
At the summer meeting (1955) of the American Mathematical Society, Mary E. Rudin presented an example of a separable normal nonparacompact space. It is the purpose of this note to point out that an example [3] due to F. B. Jones (1937) with an obvious definition of open sets is also such an example. Jones' paper was published before the notion of paracompactness appeared in the literature. The ...
متن کاملOn the paracompactness of frames
Through the study of frame congruences, new characterizations of the paracompactness of frames are obtained.
متن کاملA Note on Raghavan-reilly’s Pairwise Paracompactness
The bitopological unstability of RR-pairwise paracompactness in presence of pairwise Hausdorff separation axiom is caused by a bitopological property which is much weaker and more local than RR-pairwise paracompactness. We slightly generalize some Michael’s constructions and characterizeRR-pairwise paracompactness in terms of bitopological θ-regularity, and some other weaker modifications of pa...
متن کاملCountable Paracompactness and Weak Normality Properties By
After proving this theorem, we obtain similar results for the topological spaces studied in [7] and [11]. Also, cogent examples are given and the relation this note bears to the work of others is discussed. We shall follow the terminology of [5] except we shall assume separation properties for a space only when these assumptions are explicitly stated. For an infinite cardinal m, a set A in a to...
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ژورنال
عنوان ژورنال: Filomat
سال: 2019
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1917645a