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On topological and algebraic structure of extremally disconnected semitopological groups

Aleksander V. Arhangel'skii (2000)

Commentationes Mathematicae Universitatis Carolinae

Starting with a very simple proof of Frol’ık’s theorem on homeomorphisms of extremally disconnected spaces, we show how this theorem implies a well known result of Malychin: that every extremally disconnected topological group contains an open and closed subgroup, consisting of elements of order 2 . We also apply Frol’ık’s theorem to obtain some further theorems on the structure of extremally disconnected topological groups and of semitopological groups with continuous inverse. In particular, every...

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