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  • ▫$\mathfrak P_0$▫-spaces
    Banakh, Taras, 1968-
    A regular topological space ▫$X$▫ is defined to be a ▫$\mathfrak{P}_0$▫-space if it has countable Pytkeev network. A network ▫$\mathcal N$▫ for ▫$X$▫ is called a Pytkeev network if for any point ▫$x ... \in X$▫, neighborhood ▫$O_x \subset X$▫ of ▫$x$▫ and subset ▫$A \subset X$▫ accumulating at a ▫$x$▫ there is a set ▫$N \in \mathcal{N}$▫ such that ▫$N \subset O_x$▫ and ▫$N \cap A$▫ is infinite. The class of ▫$\mathfrak{P}_0$▫-spaces contains all metrizable separable spaces and is (properly) contained in the Michael's class of ▫$\aleph_0$▫-spaces. It is closed under many topological operations: taking subspaces, countable Tychonoff products, small countable box-products, countable direct limits, hyperspaces of compact subsets. For an ▫$\aleph_0$▫-space ▫$X$▫ and a ▫$\mathfrak{P}_0$▫-space ▫$Y$▫ the function space ▫$C_k(X,Y)$▫ endowed with the compact-open topology is a ▫$\mathfrak{P}_0$▫-space. For any sequential ▫$\aleph_0$▫-space ▫$X$▫ the free abelian topological group ▫$A(X)$▫ and the free locally convex linear topological space ▫$L(X)$▫ both are ▫$\mathfrak{P}_0$▫-spaces. A sequential space is a ▫$\mathfrak{P}_0$▫-space if and only if it is an ▫$\aleph_0$▫-space. A topological space is metrizable and separable if and only if it is a ▫$\mathfrak{P}_0$▫-space with countable fan tightness.
    Vir: Topology and its Applications. - ISSN 0166-8641 (Vol. 195, 2015, str. 151-173)
    Vrsta gradiva - članek, sestavni del
    Leto - 2015
    Jezik - angleški
    COBISS.SI-ID - 17481049

    Povezava(-e):

    http://dx.doi.org/10.1016/j.topol.2015.09.016

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