On certain optimal homeomorphisms between closed curves

Cerri, Andrea ; Di Fabio , Barbara (2010) On certain optimal homeomorphisms between closed curves. [Preprint]

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Abstract

The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between shape properties of topological spaces, modeled as continuous real-valued functions defined on the spaces themselves. Roughly speaking, the natural pseudo-distance is defined as the infimum of the change of the functions' values, when moving from one space to the other through homeomorphisms, if possible. In this paper, we prove the first available result about the existence of optimal homeomorphisms between closed curves, i.e. inducing a change of the function that equals the natural pseudo-distance.

Abstract
Document type
Preprint
Creators
CreatorsAffiliationORCID
Cerri, Andrea
Di Fabio , Barbara
Additional Information
2010 Mathematics Subject Classification. Primary 57S05, 57S10; Secondary 54C30, 68U05.
Keywords
Natural pseudo-distance, measuring function, Morse function, Size Theory.
Subjects
DOI
Deposit date
04 Aug 2010 08:36
Last modified
16 May 2011 12:14
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