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Keywords:
non-normality point; butterfly-point; nice family; nice space; metrizable crowded space; Sorgenfrey line
non-normality point; butterfly-point; nice family; nice space; metrizable crowded space; Sorgenfrey line
Summary:
J. Terasawa in "$\beta X-\{p\}$ are non-normal for non-discrete spaces $X$" (2007) and the author in "On non-normality points and metrizable crowded spaces" (2007), independently showed for any metrizable crowded space $X$ that each point $p$ of its Čech--Stone remainder $X^{*}$ is a non-normality point of $\beta X$. We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space.
References:
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