The number of translates of a closed nowhere dense set required to cover a Polish group

Annals of Pure and Applied Logic 140 (1):52-59 (2006)
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Abstract

For a Polish group let be the minimal number of translates of a fixed closed nowhere dense subset of required to cover . For many locally compact this cardinal is known to be consistently larger than which is the smallest cardinality of a covering of the real line by meagre sets. It is shown that for several non-locally compact groups . For example the equality holds for the group of permutations of the integers, the additive group of a separable Banach space with an unconditional basis and the group of homeomorphisms of various compact spaces

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References found in this work

Iterated Perfect-Set Forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
Iterated Perfectset Forcing.J. E. Baumgartner - 1979 - Annals of Mathematical Logic 17 (3):271.

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