Sergei Logunov
On butterfly-points in \beta X, Tychonoff products and weak Lindelöf numbers

Comment.Math.Univ.Carolin. 63,3 (2022) 379-383.

Abstract: Let X be the Tychonoff product \prod _{\alpha <\tau}X_{\alpha} of \tau-many Tychonoff non-single point spaces X_{\alpha}. Let p\in X^{*} be a point in the closure of some G\subset X whose weak Lindelöf number is strictly less than the cofinality of \tau. Then we show that \beta X\setminus \{p\} is not normal. Under some additional assumptions, p is a butterfly-point in \beta X. In particular, this is true if either X=\omega^{\tau} or X=R^{\tau} and \tau is infinite and not countably cofinal.

Keywords: Butterfly-point; non-normality point; Čech-Stone compactification; Tychonoff product; weak Lindelöf number

DOI: DOI 10.14712/1213-7243.2022.023
AMS Subject Classification: 54D15 54D35 54D40 54D80 54E35 54G20