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

• Autorzy: Todor Tsankov
• Języki publikacji: 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.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites
• 54H15: Transformation groups and semigroups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 3
• Strony: 269-284

Daty

wydano

2006

Twórcy

autor

Todor Tsankov

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

Identyfikatory

DOI

10.4064/fm189-3-4