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Lonely points in $ω^*$

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 $ω^*$.