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A regular non-weakly discretely generated \(P\)-space

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Abstract

We construct a consistent example of a topological space \(Y= {X \cup \{\infty\}} \) such that:

(1) \(Y\) is regular.

(2) Every \(G_\delta\) subset of \(Y\) is open.

(3) The point \(\infty\) is not isolated, but it is not in the closure of any discrete subset of \(X\).

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Authors and Affiliations

  1. Dipartimento di Ingegneria, Universitá degli Studi di Palermo, viale delle Scienze 8, 90128, Palermo, Italy

    S. Spadaro

  2. Department of Mathematics, Faculty of Science and Engineering, York University, Toronto, ON M3J 1P3, Canada

    P. Szeptycki

Authors
  1. S. Spadaro
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  2. P. Szeptycki
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Corresponding author

Correspondence to S. Spadaro.

Additional information

The first author is grateful to INdAM-GNSAGA for partial financial support.

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Spadaro, S., Szeptycki, P. A regular non-weakly discretely generated \(P\)-space. Acta Math. Hungar. 166, 92–96 (2022). https://doi.org/10.1007/s10474-022-01214-5

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  • DOI: https://doi.org/10.1007/s10474-022-01214-5

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