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On absolute retracts of ω*

A. Bella, A. Błaszczyk, A. Szymański (1994)

Fundamenta Mathematicae

An extremally disconnected space is called an absolute retract in the class of all extremally disconnected spaces if it is a retract of any extremally disconnected compact space in which it can be embedded. The Gleason spaces over dyadic spaces have this property. The main result of this paper says that if a space X of π-weight ω 1 is an absolute retract in the class of all extremally disconnected compact spaces and X is homogeneous with respect to π-weight (i.e. all non-empty open sets have the same...

On the existence of true uniform ultrafilters

Petr Simon (2004)

Commentationes Mathematicae Universitatis Carolinae

We shall show that there is an ultrafilter on singular κ with countable cofinality, which cannot be reached from the set of all subuniform ultrafilters by iterating the closure of sets of size < κ .

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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