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Examples of not continuous actions of a group in a compact space. (Exemples d’actions non continues d’un groupe dans un compact.) (French) Zbl 0794.22002

The object of this note is to present examples of a topological group \(G\) on a Baire space acting on a compact space in such a way that the action is separately, but not jointly, continuous. Under slightly stronger hypotheses on \(G\) the answer was known to be positive and it was an open question whether \(G\) being a Baire space sufficed. These examples provide a negative solution.

MSC:

22A15 Structure of topological semigroups
54H15 Transformation groups and semigroups (topological aspects)
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54G20 Counterexamples in general topology
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References:

[1] Lawson, J. D.,Additional notes on continuity in semitopological subsemigroup, Semigroup Forum12 (1976), 265–280. · Zbl 0327.22003 · doi:10.1007/BF02195932
[2] Ruppert, W.,Compact Semitopoligical Semigroups: An Intrinsic Theory, Lecture Notes in Math.1079, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo (1984). · Zbl 0606.22001
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