Displaying similar documents to “Topologies in -groups”

Topology from Neighbourhoods

Roland Coghetto (2015)

Formalized Mathematics

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Using Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]: If to each element x of a set X there corresponds a set B(x) of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x) is the set of neighborhoods...

Remarks on extremally disconnected semitopological groups

Igor V. Protasov (2002)

Commentationes Mathematicae Universitatis Carolinae

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Answering recent question of A.V. Arhangel'skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.