Sequential Rectifiable Spaces of Countable \(\mathrm {cs}^*\)-Character

Article

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.

Keywords

Rectifiable space Sequential space \(k_\omega \)-Space \(\mathrm {cs}^*\)-Character Topological loop Topological left-loop Topological lop 

Mathematics Subject Classification

54D55 54D50 54H10 22A22 22A30 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2016

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsIvan Franko National University of LvivLvivUkraine
  2. 2.Institute of Mathematics, Jan Kochanowski University in KielceKielcePoland
  3. 3.Faculty of Education, and Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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