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- W2760409813 abstract "Motivated by results of Juhasz and van Mill in [13], we define the cardinal invariant $wt(X)$, the weak tightness of a topological space $X$, and show that $|X|leq 2^{L(X)wt(X)psi(X)}$ for any Hausdorff space $X$ (Theorem 2.8). As $wt(X)leq t(X)$ for any space $X$, this generalizes the well-known cardinal inequality $|X|leq 2^{L(X)t(X)psi(X)}$ for Hausdorff spaces (Arhangel{cprime}skiĭ~[1],S}apirovskiĭ}~[18]) in a new direction. Theorem 2.8 is generalized further using covers by $G_kappa$-sets, where $kappa$ is a cardinal, to show that if $X$ is a power homogeneous compactum with a countable cover of dense, countably tight subspaces then $|X|leqmathfrak{c}$, the cardinality of the continuum. This extends a result in [13] to the power homogeneous setting." @default.
- W2760409813 created "2017-10-06" @default.
- W2760409813 creator A5029304622 @default.
- W2760409813 date "2017-09-23" @default.
- W2760409813 modified "2023-09-27" @default.
- W2760409813 title "On the weak tightness, Hausdorff spaces, and power homogeneous compacta" @default.
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