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 inf F(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.
No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit / P., Frosini; Landi, Claudia. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - STAMPA. - 24(2011), pp. 1654-1657.
Data di pubblicazione: | 2011 |
Titolo: | No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit |
Autore/i: | P., Frosini; Landi, Claudia |
Autore/i UNIMORE: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.aml.2011.04.007 |
Rivista: | |
Volume: | 24 |
Pagina iniziale: | 1654 |
Pagina finale: | 1657 |
Codice identificativo ISI: | WOS:000291912300006 |
Codice identificativo Scopus: | 2-s2.0-79957551108 |
Citazione: | No embedding of the automorphisms of a topological space into a compact metric space endows them with a composition that passes to the limit / P., Frosini; Landi, Claudia. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - STAMPA. - 24(2011), pp. 1654-1657. |
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