Far points and discretely generated spaces
Tom 158 / 2019
Colloquium Mathematicum 158 (2019), 233-254 MSC: Primary 54D35; Secondary 54A25, 54G12, 54D80, 03E10, 03E75. DOI: 10.4064/cm6750-10-2018 Opublikowany online: 12 August 2019
We give a partial solution to a question by Alas, Junqueira and Wilson by proving that under $\bf PFA $ the one-point compactification of a locally compact, discretely generated and countably tight space is also discretely generated. We then 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.