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Disconnection in the Alexandroff duplicate
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<p>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.</p>
Universitat Politecnica de Valencia
Title: Disconnection in the Alexandroff duplicate
Description:
<p>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.
</p>.
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