# Article

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Keywords:
nice family; $p$-filter; $p$-ultrafilter; projection; non-normality point; butterfly-point
Summary:
$\beta X-\{p\}$ is non-normal for any metrizable crowded space $X$ and an arbitrary point $p\in X^{*}$.
References:
[1] Blaszczyk A., Szymanski A.: Some nonnormal subspaces of the Čech-Stone compactifications of a discrete space. in: Proc. 8-th Winter School on Abstract Analysis, Prague, 1980.
[2] Gryzlov A.A.: On the question of hereditary normality of the space $\beta ømega \setminus ømega$. (1982), Topology and Set Theory (Udmurt. Gos. Univ., Izhevsk) 61-64 (in Russian). MR 0760274
[3] Logunov S.: On hereditary normality of compactifications. Topology Appl. (1996), 73 213-216. MR 1419794 | Zbl 0869.54029
[4] Logunov S.: On hereditary normality of zero-dimensional spaces. Topology Appl. (2000), 102 53-58. MR 1739263 | Zbl 0944.54016
[5] Logunov S.: On remote points, non-normality and $\pi$-weight $ømega _{1}$. Comment. Math. Univ. Carolin. (2001), 42 2 379-384. MR 1832156 | Zbl 1053.54031
[6] Logunov S.: On remote points and butterfly-points. (2002), 3 (26) Izvestia instituta matematiki i informatiki, Udmurt State University, Izhevsk (in Russian) 115-120.
[7] van Mill J.: An easy proof that $\beta N \setminus N \setminus \{p\}$ is non-normal. Ann. Math. Silesianea (1984), 2 81-84.
[8] Rajagopalan M.: $\beta N \setminus N \setminus \{p\}$ is not normal. J. Indian Math. Soc. (1972), 36 173-176. MR 0321012
[9] Shapirovskij B.: On embedding extremely disconnected spaces in compact Hausdorff spaces, $b$-points and weight of pointwise normal spaces. Dokl. Akad. Nauk SSSR (1975), 223 1083-1086. MR 0394609
[10] Terasawa J.: On the non-normality of $\beta X-\{ p\}$ for non-discrete spaces $X$. Topology Proc. (2003), 27 335-344. MR 2048942

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