On the Cohomology of Topological Semigroups

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Communications in Advanced Mathematical Sciences
Volume:2 Issue:3
On the Cohomology of Topological Semigroups

On the Cohomology of Topological Semigroups

Authors : Maysam MAYSAMİ SADR, Danial BOUZARJOMEHRİ AMNİEH

Pages : 206-212

Doi:10.33434/cams.515711

View : 12 | Download : 13

Publication Date : 2019-09-30

Article Type : Research Paper

Abstract :In this short note, we give some new results on continuous bounded cohomology groups of topological semigroups with values in complex field. We show that the second continuous bounded cohomology group of a compact metrizable semigroup, is a Banach space. Also, we study cohomology groups of amenable topological semigroups, and we show that cohomology groups of rank greater than one of a compact left or right amenable semigroup, are trivial. Also, we give some examples and applications about topological lattices.
Keywords : Topological semigroup, bounded cohomology, Banach homology

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