No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit

Details No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit

2010-05-06

arxiv.org/abs/1005.0921v1

Computer Science

Computational Geometry

6 pages, no figures

Scientific paper

The Hausdorff distance, the Gromov-Hausdorff, the Fr\'echet and the natural pseudo-distances are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as $\inf_\rho F(\rho)$ where $F$ is a suitable functional and $\rho$ varies in a set of correspondences containing the set of homeomorphisms. Our main result states that the set of homeomorphisms cannot be enlarged to a metric space $\mathcal{K}$, in such a way that the composition in $\mathcal{K}$ (extending the composition of homeomorphisms) passes to the limit and, at the same time, $\mathcal{K}$ is compact.

Affiliated with

Also associated with

No associations

Rating

No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-25818