Sequential rectifiable spaces of countable ▫$\mathrm{cs}^\ast$▫-character

Banakh, Taras (author), Repovš, Dušan (author)

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

Record is a part of a journal

• Title: Bulletin of the Malaysian Mathematical Sciences Society
• Shortened title: Bull. Malays. Math. Sci. Soc.
• Publisher: Springer
• ISSN: 0126-6705
• COBISS.SI-ID: 515781657