We construct a consistent example of a topological space Y= X∪ {∞} such that: (1) Y is regular. (2) Every Gδ subset of Y is open. (3) The point ∞ is not isolated, but it is not in the closure of any discretesubset of X.
Spadaro S., Szeptycki P. (2022). A regular non-weakly discretely generated P-space. ACTA MATHEMATICA HUNGARICA, 166(1), 92-96 [10.1007/s10474-022-01214-5].
A regular non-weakly discretely generated P-space
Spadaro S.
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2022-02-01
Abstract
We construct a consistent example of a topological space Y= X∪ {∞} such that: (1) Y is regular. (2) Every Gδ subset of Y is open. (3) The point ∞ is not isolated, but it is not in the closure of any discretesubset of X.
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