Article
MSC:
54D15,
54D35,
54D40,
54D80,
54E35,
54G20 | MR 4405820 | Zbl 07511577 | DOI: 10.14712/1213-7243.2021.032
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Keywords:
non-normality point; butterfly point; Kunen point; super Kunen point
non-normality point; butterfly point; Kunen point; super Kunen point
Summary:
We show that $\omega ^{*}\setminus \{p\}$ is not normal, if $p$ is a limit point of some countable subset of $\omega ^{*}$, consisting of points of character $\omega _{1}$. Moreover, such a point $p$ is a Kunen point and a super Kunen point.
References:
[1] Bešlagić A., van Douwen E. K.: Spaces of nonuniform ultrafilters in spaces of uniform ultrafilters. Topology Appl. 35 (1990), no. 2–3, 253–260. DOI 10.1016/0166-8641(90)90110-N | MR 1058805
[2] Błaszczyk A., Szymański A.: Some non-normal subspaces of the Čech–Stone compactification of a discrete space. Proc. Eighth Winter School on Abstract Analysis, Czechoslovak Academy of Sciences, Praha, 1980, pages 35–38.
[3] Comfort W. W., Negrepontis S.: Homeomorphs of three subspaces of $ \beta N\setminus N$. Math. Z. 107 (1968), 53–58. DOI 10.1007/BF01111048 | MR 0234422
[4] Fine N. J., Gillman L.: Extensions of continuous functions in $\beta N$. Bull. Amer. Math. Soc. 66 (1960), 376–381. DOI 10.1090/S0002-9904-1960-10460-0 | MR 0123291
[5] Gryzlov A. A.: On the question of hereditary normality of the space $\beta \omega \setminus \omega$. Topology and Set Theory, Udmurt. Gos. Univ., Izhevsk, 1982, 61–64 (Russian). MR 0760274
[6] Rajagopalan M.: $\beta N-N-\{p\}$ is not normal. J. Indian Math. Soc. (N.S.) 36 (1972), 173–176. MR 0321012
[7] Szymanski A.: Retracts and non-normality points. Topology Proc. 40 (2012), 195–201. MR 2832067
[8] Warren N. M.: Properties of Stone–Čech compactifications of discrete spaces. Proc. Amer. Math. Soc. 33 (1972), 599–606. MR 0292035
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