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- W2109957996 abstract "Let X be a Tychonoff space, H ( X ) the group of all self-homeomorphisms of X and e : ( f , x ) ∈ H ( X ) × X → f ( x ) ∈ X the evaluation map. Let L H ( X ) be the upper-semilattice of all group topologies on H ( X ) with the additional property that the evaluation map is continuous (ordered by inclusion). The existence of a least element in L H ( X ) has been proven for T 2 locally compact spaces, for T 2 rim-compact and locally connected spaces and for products of T 2 zero-dimensional spaces satisfying the property: any two non-empty clopen subspaces are homeomorphic . We show that X being rim-compact is not a necessary condition in order for L H ( X ) to have a least element. Let R and Q be the sets of the real and rational numbers respectively, both carrying the Euclidean topology. It is known that R × Q is not rim-compact. We prove that L H ( R × Q ) admits a least element." @default.
- W2109957996 created "2016-06-24" @default.
- W2109957996 creator A5068585929 @default.
- W2109957996 date "2009-02-01" @default.
- W2109957996 modified "2023-09-24" @default.
- W2109957996 title "Group action on <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:mi mathvariant=double-struck>R</mml:mi><mml:mo>×</mml:mo><mml:mi mathvariant=double-struck>Q</mml:mi></mml:math> and fine group topologies" @default.
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- W2109957996 doi "https://doi.org/10.1016/j.topol.2008.11.013" @default.
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