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- W1637673921 abstract "We prove that a compact connected nonmetrizable group contains a proper dense $omega$-bounded subgroup. This is then used to show that every compact nonmetrizable group $G$ can be partitioned into $|G|$-many pairwise disjoint dense topologically homogeneous $omega$-bounded subsets each of cardinal $|G|$ and each Haar nonmeasurable with full Haar outermeasure. This allows us to then generalize an observation of Kakutani and Oxtoby and to conclude that each infinite compact group $G$ may be partitioned into a collection of $|G|$-many pairwise disjoint dense subsets of full Haar outermeasure. A corollary of these results is that the Stone-Cech compactification $beta X$ of an infinite discrete space $X$ may be partitioned into $|beta X|$ pairwise disjoint $omega$-bounded subsets each of size $|beta X|$." @default.
- W1637673921 created "2016-06-24" @default.
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- W1637673921 date "1997-06-01" @default.
- W1637673921 modified "2023-10-18" @default.
- W1637673921 title "Haar nonmeasurable partitions of compact groups" @default.
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- W1637673921 doi "https://doi.org/10.21099/tkbjm/1496163176" @default.
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