The role of connectedness in the structure and the action of group of isometries of locally compact metric spaces

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dc.creatorManoussos, Antonios
dc.creatorStrantzalos, Polychronis
dc.date2000-10-09
dc.date.accessioned2026-07-07T04:37:55Z
dc.date.available2026-07-07T04:37:55Z
dc.descriptionBy proving that, if the quotient space S(X) of the connected components of the locally compact metric space (X,d) is compact, then the full group I(X,d) of isometries of X is closed in C(X,X) with respect to the pointwise topology, i.e., that I(X,d) coincides in this case with its Ellis' semigroup, we complete the proof of the following: Theorem (a) If S(X) is not compact, I(X,d) need not be locally compact, nor act properly on X. (b) If S(X) is compact, I(X,d) is locally compact but need not act properly on X. (c) If, especially, X is connected, the action (I(X,d),X) is proper.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/math/0010083
dc.identifierhttp://arxiv.org/abs/math/0010083
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60083
dc.subjectGeneral Topology
dc.subjectDynamical Systems
dc.subject54H20, 54E15 (Primary); 54H15 (Secondary)
dc.titleThe role of connectedness in the structure and the action of group of isometries of locally compact metric spaces
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