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Sequential rectifiable spaces of countable ▫$\mathrm{cs}^\ast$▫-character
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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
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
PID:
20.500.12556/RUL-109513
UDC:
515.122:517.982
ISSN on article:
0126-6705
DOI:
10.1007/s40840-016-0331-5
COBISS.SI-ID:
17637977
Publication date in RUL:
04.09.2019
Views:
796
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320
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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:
Springer Nature, Malaysian Mathematical Sciences Society, Penerbit Universiti Sains Malaysia
ISSN:
0126-6705
COBISS.SI-ID:
515781657
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