C -Paracompactness and C 2 -paracompactness

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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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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 ...

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ژورنال

عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS

سال: 2019

ISSN: 1303-6149

DOI: 10.3906/mat-1804-54