Disconnection in the Alexandroff duplicate
Submitted: 2020-11-10
|Accepted: 2021-07-08
|Published: 2021-10-01
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Keywords:
extremally disconnected space, Alexandroff duplicate, P-space
Supporting agencies:
Abstract:
It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space can ever be extremally disconnected. We answer this question in the affirmative; an example of van Douwen is significant. In a slightly different direction we also characterize when the Alexandroff duplicate of a space is a P-space as well as when it is an almost P-space.
References:
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