On butterfly-points in X , Tychonoff products and weak Lindelöf numbers

[摘要] 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.

[学科分类] 物理化学和理论化学

[关键词] Butterfly-point;non-normality point;Čech-Stone compactification;Tychonoff product;weak Lindelöf number