Locally compact spaces whose Alexandroff one-point compactifications are perfect
Lonely points revisited
In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point 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 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 . This answers the question of P. Simon...
Long chains in Rudin-Frolík order