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

Frosini, Patrizio ; Landi , Claudia (2010) No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit. DOI 10.6092/unibo/amsacta/2768.
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## Abstract

The Hausdorff distance, the Gromov-Hausdorff, the Fréchet 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 $K$, in such a way that the composition in $K$ (extending the composition of homeomorphisms) passes to the limit and, at the same time, $K$ is compact.

Abstract
Document type
Monograph (Technical Report)
Creators
CreatorsAffiliationORCID
Frosini, Patrizio
Landi , Claudia
Keywords
Space of homeomorphisms, correspondence, compact metric space
Subjects
DOI
Deposit date
06 May 2010 10:12