  We give a partial solution to a question by Alas, Junqueria and Wilson by
proving that under PFA the one-point compactification of a locally compact,
discretely generated and countably tight space is also discretely generated.
After this, we study the cardinal number given by the smallest possible
character of remote and far sets of separable metrizable spaces. Finally, we
prove that in some cases a countable space has far points.
