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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Vasyl Stefanyk Precarpathian National University
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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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1724673534773428224 |