Lonely points in ${\omega }^{\ast }$

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 ${\omega }^{\ast }$ 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 ${\omega }^{\ast }$ and show why known methods do not allow us to construct them in all of ${\omega }^{\ast }$.

Cited by in corpus (1)

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