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Sequential rectifiable spaces of countable ▫$\mathrm{cs}^\ast$▫-character
ID Banakh, Taras (Author), ID Repovš, Dušan (Author)

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Abstract
We prove that each non-metrizable sequential rectifiable space ▫$X$▫ of countable ▫$\mathrm{cs}^\ast$▫-character contains a clopen rectifiable submetrizable ▫$k_\omega$▫-subspace ▫$H$▫ and admits a disjoint cover by open subsets homeomorphic to clopen subspaces of ▫$H$▫. This implies that each sequential rectifiable space of countable ▫$\mathrm{cs}^\ast$▫-character is either metrizable or a topological sum of submetrizable ▫$k_\omega$▫-spaces. Consequently, ▫$X$▫ is submetrizable and paracompact. This answers a question of Lin and Shen posed in 2011.

Language:English
Keywords:rectifiable space, sequential space, $k_\omega$-space, cs*-character, topological loop, topological left-loop, topological lop
Work type:Article (dk_c)
Typology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
FMF - Faculty of Mathematics and Physics
Year:2017
Number of pages:Str. 975-993
Numbering:Vol. 40, iss. 3
UDC:515.122:517.982
ISSN on article:0126-6705
DOI:10.1007/s40840-016-0331-5 This link opens in a new window
COBISS.SI-ID:17637977 This link opens in a new window
Publication date in RUL:04.09.2019
Views:347
Downloads:170
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Record is a part of a journal

Title:Bulletin of the Malaysian Mathematical Sciences Society
Shortened title:Bull. Malays. Math. Sci. Soc.
Publisher:Malaysian Mathematical Society.
ISSN:0126-6705
COBISS.SI-ID:515781657 This link opens in a new window

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