On non-normality points, Tychonoff products and Suslin number

Abstract

Let a space $X$ be Tychonoff product $\prod_{\alpha <\tau}X_{\alpha}$ of $\tau$-many Tychonoff nonsingle point spaces $X_{\alpha}$. Let Suslin number of $X$ be strictly less than the cofinality of $\tau$. Then we show that every point of remainder is a non-normality point of its Čech--Stone compactification $\beta X$. In particular, this is true if $X$ is either $R^{\tau}$ or $\omega ^{\tau}$ and a cardinal $\tau$ is infinite and not countably cofinal.