Supercompactness of spaces of capacities and its consequences

Supercompactness of spaces of capacities and its consequences

It is proved that the space of normalized real-valued capacities on an openly generated compactum is an absolute retract. Existence of a normal binary subbase for closed subsets in the space of normalized lattice-valued capacities on an openly generated compactum is also shown, which implies that th...

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Main Author: T.M. Cherkovskyi
Format: Article
Language:English
Published: Vasyl Stefanyk Precarpathian National University 2013-06-01
Series:Karpatsʹkì Matematičnì Publìkacìï
Subjects:
supercompactness
capacity
dugundji space
absolute retract
Online Access:https://journals.pnu.edu.ua/index.php/cmp/article/view/3663
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spelling doaj-80a676515f7b4ba580ccc8abe2d1bb6d2020-11-25T03:06:35ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102013-06-015114314910.15330/cmp.5.1.143-1493663Supercompactness of spaces of capacities and its consequencesT.M. Cherkovskyi0Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineIt is proved that the space of normalized real-valued capacities on an openly generated compactum is an absolute retract. Existence of a normal binary subbase for closed subsets in the space of normalized lattice-valued capacities on an openly generated compactum is also shown, which implies that this space is a Dugundji space.https://journals.pnu.edu.ua/index.php/cmp/article/view/3663supercompactnesscapacitydugundji spaceabsolute retract
collection DOAJ
language English
format Article
sources DOAJ
author T.M. Cherkovskyi
spellingShingle T.M. Cherkovskyi
Supercompactness of spaces of capacities and its consequences
Karpatsʹkì Matematičnì Publìkacìï
supercompactness
capacity
dugundji space
absolute retract
author_facet T.M. Cherkovskyi
author_sort T.M. Cherkovskyi
title Supercompactness of spaces of capacities and its consequences
title_short Supercompactness of spaces of capacities and its consequences
title_full Supercompactness of spaces of capacities and its consequences
title_fullStr Supercompactness of spaces of capacities and its consequences
title_full_unstemmed Supercompactness of spaces of capacities and its consequences
title_sort supercompactness of spaces of capacities and its consequences
publisher Vasyl Stefanyk Precarpathian National University
series Karpatsʹkì Matematičnì Publìkacìï
issn 2075-9827
2313-0210
publishDate 2013-06-01
description It is proved that the space of normalized real-valued capacities on an openly generated compactum is an absolute retract. Existence of a normal binary subbase for closed subsets in the space of normalized lattice-valued capacities on an openly generated compactum is also shown, which implies that this space is a Dugundji space.
topic supercompactness
capacity
dugundji space
absolute retract
url https://journals.pnu.edu.ua/index.php/cmp/article/view/3663
work_keys_str_mv AT tmcherkovskyi supercompactnessofspacesofcapacitiesanditsconsequences
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