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arXiv · 1607.06270

Lonely points in $ω^*$

Jonathan L. Verner
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Abstract

Inspired by the work of J. van Mill we define a new topological type --- lonely points. We show that the question of whether these points exist in $ω^*$ is equivalent to finding a countable OHI, extremally disconnected, zerodimensional space with a remote weak P-point. We also present methods which allow us to find lonely points in a large subspace of $ω^*$ and show why known methods do not allow us to construct them in all of $ω^*$.

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Jonathan L. Verner. 2016-07-21. Lonely points in $ω^*$. https://doi.org/10.1016/j.topol.2008.05.020

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