Abstract: 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.
Keywords: non-normality point; butterfly-point; nice family; nice space; metrizable crowded space; Sorgenfrey line
DOI: DOI 10.14712/1213-7243.2021.019
AMS Subject Classification: 54D15 54D35 54D40 54D80 54E35 54G20