Lonely points revisited

Verner, Jonathan L.

Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 1, pp. 105-110.

Résumé

In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point $p\in X$ is lonely if it is a limit point of a countable dense-in-itself set, it is not a limit point of a countable discrete set and all countable sets whose limit point it is form a filter. We use the space ${\mathcal G}_\omega$ from a paper of A. Dow, A.V. Gubbi and A. Szymański [Rigid Stone spaces within ZFC, Proc. Amer. Math. Soc. 102 (1988), no. 3, 745--748] to construct lonely points in $\omega^*$. This answers the question of P. Simon posed in our paper Lonely points in $\omega^*$, Topology Appl. 155 (2008), no. 16, 1766--1771.

Détail

Classification : 54D40, 54D80, 54G05
Keywords: $\beta\omega$; lonely point; weak P-point; irresolvable spaces