The Degree of Weakly Discretely Generated Spaces

A regular non-weakly discretely generated $$P$$-space

“…They also proved that if X is a Lindelöf P -space where every linearly Lindelöf subspace is Lindelöf then X is weakly discretely generated. More results about discrete generability of P -spaces appear in the article [2] by the same authors.…”

Remote Filters and Discretely Generated Spaces

“…1.2. Question (Alas, Junqueira and Wilson, [2]) Is there a locally compact Hausdorff discretely generated space with its one point compactification not discretely generated?…”

Far points and discretely generated spaces

“…Is the one-point compactification of X also discretely generated?So far, this question has been answered consistently in the negative. First countable counterexamples have been constructed using CH [2] or the existence of a Souslin line [1]. Later, it was shown in [17] that a similar construction could be carried out assuming the cardinal equation p = cof (M); the resulting space has an Date: October 15, 2018.…”

“…First countable spaces are clearly discretely generated and in fact spaces with relatively rich structures are discretely generated. For example, it has been shown that countable products and box products of monotonically normal spaces are discretely generated ([21], [2]). Also, notice that the definitions of discretely generated and weakly discretely generated spaces are similar to the classic notions of Frechét-Urysohn spaces and sequential spaces, respectively, with the advantage that there is no bound for tightness (see Example 3.5 and Proposition 3.6 in [14]).If one focuses on compact spaces, there are interesting things to say.…”