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  • On ▫$\kappa$▫-bounded and $M$-compact reflections of topological spaces
    Banakh, Taras, 1968-
    For a topological space ▫$X$▫ its reflection in a class ▫$\mathsf{T}$▫ of topological spaces is a pair ▫$(\mathsf{T} X, i_X)$▫ consisting of a space ▫$\mathsf{T} X \in \mathsf{T}$▫ and continuous map ... ▫$i_X:X\to \mathsf{T} X$▫ such that for any continuous map ▫$f:X \to Y$▫ to a space ▫$Y \in \mathsf{T}$▫ there exists a unique continuous map ▫$\bar{f}: \mathsf{T} X \to Y$▫ such that ▫$f=\bar{f}\circ i_X$▫. In this paper for an infinite cardinal ▫$\kappa$▫ and a nonempty set ▫$M$▫ of ultrafilters on ▫$\kappa$▫, we study the reflections of topological spaces in the classes ▫$\mathsf{H}_\kappa$▫ of ▫$\kappa$▫-bounded Hausdorff spaces and ▫$\mathsf{H}_M$▫ of ▫$M$▫-compact Hausdorff spaces (a topological space ▫$X$▫ is ▫$\kappa$▫-bounded if the closures of subsets of cardinality ▫$\le\ kappa$▫ in ▫$X$▫ are compact; ▫$X$▫ is ▫$M$▫-compact if any function ▫$x: \kappa \to X$▫ has a ▫$p$▫-limit in ▫$M$▫ for every ultrafilter ▫$p\in M$▫).
    Vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 289, Feb. 2021, art. 107547 (20 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2021
    Jezik - angleški
    COBISS.SI-ID - 45537027

    Povezava(-e):

    https://doi.org/10.1016/j.topol.2020.107547
    DOI

vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 289, Feb. 2021, art. 107547 (20 str.))
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