Sequential rectifiable spaces of countable ▫$\mathrm{cs}^\ast$▫-characterBanakh, Taras (Avtor) Repovš, Dušan (Avtor) rectifiable spacesequential space$k_\omega$-spacecs*-charactertopological looptopological left-looptopological lopWe 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 2011.20172019-09-04 14:50:59Članek v reviji109513sl