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

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 rectifiable space, sequential space, $k_\omega$-space, cs*-character, topological loop, topological left-loop, topological lop Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of EducationFMF - Faculty of Mathematics and Physics 2017 Str. 975-993 Vol. 40, iss. 3 515.122:517.982 0126-6705 10.1007/s40840-016-0331-5 17637977 04.09.2019 347 170 AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Bulletin of the Malaysian Mathematical Sciences Society Bull. Malays. Math. Sci. Soc. Malaysian Mathematical Society. 0126-6705 515781657

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