Embedding topological spaces into Hausdorff $\kappa$-bounded spaces

Autor:	Banakh, T., Bardyla, S., Ravsky, A.
Rok vydání:	2019
Předmět:	Mathematics - General Topology 54D30 54D35 54D80 54B30
Druh dokumentu:	Working Paper
Popis:	Let $\kappa$ be an infinite cardinal. A topological space $X$ is $\kappa$-bounded if the closure of any subset of cardinality $\le\kappa$ in $X$ is compact. We discuss the problem of embeddability of topological spaces into Hausdorff (Urysohn, regular) $\kappa$-bounded spaces, and present a canonical construction of such an embedding. Also we construct a (consistent) example of a sequentially compact separable regular space that cannot be embedded into a Hausdorff $\omega$-bounded space. Comment: 11 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.00185 Zobrazit plný text záznamu View this record from Arxiv