The Hausdorff distance, the Gromov-Hausdorff, the Fréchet and the natural pseudo-distance are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as infρF(ρ) where F is a suitable functional and ρ 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.
Patrizio Frosini, Claudia Landi (2011). No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit. APPLIED MATHEMATICS LETTERS, 24, 1654-1657 [10.1016/j.aml.2011.04.007].
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
2011
Abstract
The Hausdorff distance, the Gromov-Hausdorff, the Fréchet and the natural pseudo-distance are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as infρF(ρ) where F is a suitable functional and ρ 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
