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.
Full text available as:
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
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.
Document type
Monograph
(Technical Report)
Creators
Keywords
Space of homeomorphisms, correspondence, compact metric
space
Subjects
DOI
Deposit date
06 May 2010 10:12
Last modified
16 May 2011 12:13
URI
Other metadata
Document type
Monograph
(Technical Report)
Creators
Keywords
Space of homeomorphisms, correspondence, compact metric
space
Subjects
DOI
Deposit date
06 May 2010 10:12
Last modified
16 May 2011 12:13
URI
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