New algebras of functions on topological groups arising from G-spaces

• Autorzy: E. Glasner , M. Megrelishvili
• Języki publikacji: EN

Abstrakty

EN

For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. We show that SUC(G) contains the algebra WAP(G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and Asplund functions respectively. For the Polish groups of order preserving homeomorphisms of the unit interval and of isometries of the Urysohn space of diameter 1, we show that SUC(G) is trivial. We introduce the notion of fixed point on a class P of flows (P - fpp) and study in particular groups with the SUC-fpp. We study the Roelcke algebra (= UC(G) = right and left uniformly continuous functions) and SUC compactifications of the groups S(ℕ), of permutations of a countable set, and H(C), of homeomorphisms of the Cantor set. For the first group we show that WAP(G) = SUC(G) = UC(G) and also provide a concrete description of the corresponding metrizable (in fact Cantor) semitopological semigroup compactification. For the second group, in contrast, we show that SUC(G) is properly contained in UC(G). We then deduce that for this group UC(G) does not yield a right topological semigroup compactification.

Kategorie tematyczne

• 54H20: Topological dynamics
• 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
• 54H15: Transformation groups and semigroups
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2008
• Tom: 201
• Numer: 1
• Strony: 1-51

Daty

wydano

2008

Twórcy

autor

E. Glasner

• Department of Mathematics, Tel-Aviv University, Ramat Aviv, Israel

autor

M. Megrelishvili

• Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel

Identyfikatory

DOI

10.4064/fm201-1-1