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Lonely points revisited

Jonathan L. Verner (2013)

Commentationes Mathematicae Universitatis Carolinae

In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point p 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 𝒢 ω 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 ω * . This answers the question of P. Simon...

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