Properties of Topologies for the Continuous Representability of All Weakly Continuous Preorders

Autor:	Gianni Bosi, Laura Franzoi, Gabriele Sbaiz
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	strongly useful topology weakly continuous preorder hereditarily separable topology Lindelöf property Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 20, p 4335 (2023)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11204335
Popis:	We investigate properties of strongly useful topologies, i.e., topologies with respect to which every weakly continuous preorder admits a continuous order-preserving function. In particular, we prove that a topology is strongly useful provided that the topology generated by every family of separable systems is countable. Focusing on normal Hausdorff topologies, whose consideration is fully justified and not restrictive at all, we show that strongly useful topologies are hereditarily separable on closed sets, and we identify a simple condition under which the Lindelöf property holds.
Databáze:	Directory of Open Access Journals
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