Sequential rectifiable spaces of countable $c{s}^{\ast }$-character

Abstract

We prove that each non-metrizable sequential rectifiable space $X$ of countable $c{s}^{\ast }$-character contains a clopen rectifiable submetrizable $k_{\omega }$-subspace $H$ and admits an open disjoint cover by subspaces homeomorphic to clopen subspaces of $H$. This implies that each sequential rectifiable space with countable $c{s}^{\ast }$-character either is metrizable or else is 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.

12 pages

References in corpus (1)

• On rectifiable spaces and paratopological groups

Cited by in corpus (1)

• The strong Pytkeev property in topological spaces