Swelling actions of \(\Gamma\)-compact semigroups
type: Item
instance of: scholarly article
title: Swelling actions of \(\Gamma\)-compact semigroups
zbMATH Open document ID: 0582.22001
DOI: 10.1007/BF02573183
published in: Semigroup Forum
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134794
review text: The authors discuss conditions which insure that an action of a topological semigroup on a Hausdorff space will allow no closed set to be swelled by a compact element of the acting semigroup. They develop and employ the concept of t-sequence along with an analog of the classical Weil lemma. Topological groups and the role of the bicyclic semigroup in swelling is also part of the discussion. A swelling \(\Gamma\)-compact action which is minimal in the sense that each \(\Gamma\)-compact action contains a subaction which has this action as a continuous homomorphic image is constructed. Moreover, this is a characterization of swelling \(\Gamma\)-compact actions. From this result it is shown that the class of \(\Gamma\)-compact c-stable (non-swelling) actions is closed under products and proper closed continuous homomorphisms.
Mathematics Subject Classification ID: 22A99
Mathematics Subject Classification ID: 22A25
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 3931296
zbMATH Keywords: swelling action
zbMATH Keywords: \(\Gamma \) -compact semigroup
zbMATH Keywords: c-stable action
zbMATH Keywords: topological group
zbMATH Keywords: regular semigroup
zbMATH Keywords: topological semigroup
zbMATH Keywords: t-sequence
zbMATH Keywords: bicyclic semigroup
author: John A. Hildebrant
author: Robert Jacob Koch
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3931296