Abstract
We prove that each non-metrizable sequential rectifiable space X of countable \(\mathrm {cs}^*\)-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 \(\mathrm {cs}^*\)-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.
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Communicated by Rosihan M. Ali, Dato’.
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Banakh, T., Repovš, D. Sequential Rectifiable Spaces of Countable \(\mathrm {cs}^*\)-Character. Bull. Malays. Math. Sci. Soc. 40, 975–993 (2017). https://doi.org/10.1007/s40840-016-0331-5
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DOI: https://doi.org/10.1007/s40840-016-0331-5
Keywords
- Rectifiable space
- Sequential space
- \(k_\omega \)-Space
- \(\mathrm {cs}^*\)-Character
- Topological loop
- Topological left-loop
- Topological lop