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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2006 | 189 | 3 | 269-284

## Compactifications of ℕ and Polishable subgroups of $S_{∞}$

EN

### Abstrakty

EN
We study homeomorphism groups of metrizable compactifications of ℕ. All of those groups can be represented as almost zero-dimensional Polishable subgroups of the group $S_{∞}$. As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of $S_{∞}$. We prove a sufficient condition for these groups to be one-dimensional and also study their descriptive complexity. In the last section we associate with every Polishable ideal on ℕ a certain Polishable subgroup of $S_{∞}$ which shares its topological dimension and descriptive complexity.

269-284

wydano
2006

### Twórcy

autor
• Department of Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, U.S.A.