The natural pseudo-distance as a quotient pseudo-metric, and applications

Cagliari, Francesca ; Di Fabio, Barbara ; Landi, Claudia (2012) The natural pseudo-distance as a quotient pseudo-metric, and applications. [Preprint]
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Abstract

The natural pseudo-distance is a similarity measure conceived for the purpose of comparing shapes. In this paper we revisit this pseudo-distance from the point of view of quotients. In particular, we show that the natural pseudo-distance coincides with the quotient pseudo-metric on the space of continuous functions on a compact manifold, endowed with the uniform convergence metric, modulo self-homeomorphisms of the manifold. As applications of this result, the natural pseudo-distance is shown to be actually a metric on a number of function subspaces such as the space of topological embeddings, of isometries, and of simple Morse functions on surfaces.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Cagliari, Francesca
Di Fabio, Barbara
Landi, Claudia
Keywords
Function space, Morse function, homeomorphism group action, isometry, shape comparison
Subjects
DOI
Deposit date
10 Oct 2012 08:31
Last modified
29 Jan 2013 10:24
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