Bulletin of the Belgian Mathematical Society - Simon Stevin

Topological groups have representable actions

Francesca Cagliari and Maria Manuel Clementino

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This paper shows that the group of auto-homeomorphisms of a topological group can be endowed with a topology so that the resulting topological group plays, for topological groups, the role of the group of automorphisms of a group: it represents the internal actions on the given topological group.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 4 (2019), 519-526.

First available in Project Euclid: 13 December 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms 54H11: Topological groups [See also 22A05] 22A05: Structure of general topological groups 18B30: Categories of topological spaces and continuous mappings [See also 54-XX]

topological group representability of actions split extension classifier group of homeomorphisms Stone-Čech compactification


Cagliari, Francesca; Clementino, Maria Manuel. Topological groups have representable actions. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 4, 519--526. doi:10.36045/bbms/1576206354. https://projecteuclid.org/euclid.bbms/1576206354

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