Disconnection in the Alexandroff duplicate

Papiya Bhattacharjee; Michelle L. Knox; Warren Wm. McGovern

doi:10.4995/agt.2021.14602

Authors

Papiya Bhattacharjee Florida Atlantic University
Michelle L. Knox Midwestern State University
Warren Wm. McGovern Florida Atlantic University

DOI:

https://doi.org/10.4995/agt.2021.14602

Keywords:

extremally disconnected space, Alexandroff duplicate, P-space

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.

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Author Biographies

Papiya Bhattacharjee, Florida Atlantic University

Department of Mathematical Sciences

Warren Wm. McGovern, Florida Atlantic University

Professor of Mathematics
Wilkes Honors College

References

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