20.500.12556/RUL-109513 Sequential rectifiable spaces of countable ▫$\mathrm{cs}^\ast$▫-character 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. rectifiable space sequential space $k_\omega$-space cs*-character topological loop topological left-loop topological lop true false true Angleški jezik Ni določen Članek v reviji 2019-09-04 14:50:59 2019-09-04 14:51:00 2022-08-21 03:42:39 0000-00-00 00:00:00 2017 0 0 Str. 975-993 iss. 3 Vol. 40 July 2017 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.122:517.982 0126-6705 10.1007/s40840-016-0331-5 17637977 515781657 RAZ_Banakh_Taras_i2017.pdf RAZ_Banakh_Taras_i2017.pdf 1 60B9A25E6D1351DF3D208E33C6B1740C db945f549cf5e5b3239f880b62d71559dfd62ab3125a150bab990adefeafe9ee e2f22789-a1b6-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=121093 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0