Cerri, Andrea ; Di Fabio , Barbara
OPTIMAL HOMEOMORPHISMS BETWEEN CLOSED CURVES.
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Abstract
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. 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
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. 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.
Document type
Preprint
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Keywords
Natural pseudo-distance, measuring function, Morse function, Size Theory.
Subjects
Deposit date
22 Sep 2009 07:45
Last modified
16 May 2011 12:11
URI
Other metadata
Document type
Preprint
Creators
Keywords
Natural pseudo-distance, measuring function, Morse function, Size Theory.
Subjects
Deposit date
22 Sep 2009 07:45
Last modified
16 May 2011 12:11
URI
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OPTIMAL HOMEOMORPHISMS BETWEEN CLOSED CURVES. (deposited 22 Sep 2009 07:45)
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