JournalsggdVol. 7, No. 2pp. 475–493

Chain recurrence in β\beta -compactifications of topological groups

  • Josiney A. Souza

    Universidade Estadual de Maringá, Maringá, Brazil
Chain recurrence in $\beta $-compactifications of topological groups cover
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Abstract

Let GG be a topological group. In this paper limit behavior in the Stone–Čech compactification βG\beta G is studied. It depends on a family of translates of a reversible subsemigroup SS. The notion of semitotal subsemigroup is introduced. It is shown that the semitotality property is equivalent to the existence of only two maximal chain transitive sets in % \beta G whenever SS is centric. This result links an algebraic property to a dynamical property. The concept of a chain recurrent function is also introduced and characterized via the compactification βG\beta G. Applications of chain recurrent function to linear differential systems and transformation groups are done.

Cite this article

Josiney A. Souza, Chain recurrence in β\beta -compactifications of topological groups. Groups Geom. Dyn. 7 (2013), no. 2, pp. 475–493

DOI 10.4171/GGD/191