×

zbMATH — the first resource for mathematics

On supercomplete uniform spaces. IV: Countable products. (English) Zbl 0713.54027
[For part I-II see Zbl 0538.54015, Zbl 0654.54020.]
Generally the product of paracompact spaces is not paracompact, but it is known that it is true for the countable product of locally compact paracompact spaces and for paracompact p-spaces. The author proves that the countable product of supercomplete C-scattered spaces is supercomplete. Supercompleteness was introduced by J. R. Isbell in Pac. J. Math. 12, 287-290 (1962; Zbl 0104.395) and can be considered as a uniform version of paracompactness. A uniform space \(\mu\) X is called supercomplete if the hyperspace of closed subsets H(\(\mu\) X) equipped with the Hausdorff uniformity is a complete uniform space.
Reviewer: R.Welk

MSC:
54E15 Uniform structures and generalizations
54B10 Product spaces in general topology
54B20 Hyperspaces in general topology
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54G12 Scattered spaces
PDF BibTeX XML Cite
Full Text: DOI EuDML