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- W1551899496 abstract "By proving that, if the quotient space S(X) of the connected components ofthe 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 completethe 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." @default.
- W1551899496 created "2016-06-24" @default.
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- W1551899496 date "2000-10-09" @default.
- W1551899496 modified "2023-09-27" @default.
- W1551899496 title "The role of connectedness in the structure and the action of group of isometries of locally compact metric spaces" @default.
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