Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8946337 | Topology and its Applications | 2018 | 21 Pages |
Abstract
By Fn(X), nâ¥1, we denote the n-th symmetric product of a metric space (X,d) as the space of the nonempty finite subsets of X with at most n elements endowed with the Hausdorff metric dH. By Iso(X) we denote the group of all isometries from X onto itself with the topology of pointwise convergence. In this paper, we show that, under the certain hypothesis, Iso(Fn(X)) is topologically isomorphic to the semidirect product group Iso(Fn(X),F1(X))âIso(X). We apply those results to âpq, (p,q)â[1,â]ÃNâ¥2â, as particular spaces and prove the following statements:
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Naotsugu Chinen,