Dense topological groups in Parovičenko spaces
Keywords:
$P$-space, Parovičenko space, $G_\delta$-topology, $\pi$-character, homogeneous, coset space, almost $P$-space, topological groupAbstract
We show that the statement 'the Cech-Stone remainder of the discrete space $\omega$ contains a dense subspace which is (homeomorphic to) a topological group' is not a statement of ZFC. We also discuss the question of whether this result can be extended to Parovičenko spaces.
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