In our previous paper, Lonely points, 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, not a limit point a countable discrete set and all countable sets whose limit point it is, form a filter. We use the space Gω from a paper of A.

Dow, A.V. Gubbi and A.

Szymański (DGS88) to construct lonely points in ω∗. This answers the question of P.

Simon posed in our paper Lonely points (Ver08).