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Lipschitz quotient mappings with good ratio of constants
Author(s) -
Maleva Olga
Publication year - 2002
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300016144
Subject(s) - lipschitz continuity , mathematics , quotient , bijection , cardinality (data modeling) , pure mathematics , point (geometry) , mathematical analysis , combinatorics , geometry , computer science , data mining
It is shown that Lipschitz quotient mappings between finite dimensional spaces behave nicely ( e.g. , are bijective in the case of equal dimensions) if the Lipschitz and co‐Lipschitz constants are close to each other. For Lipschitz quotient mappings of the plane, a bound for the cardinality of the pre‐image of a point in terms of the ratio of the constants is obtained.