FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 1, PAGES 19-32
B. G. Averbuh
Abstract
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Arbitrary transformations of a family of pseudometrics are studied which
result in uniform continuous pseudometrics again. Then their properties
are applied for a description of a quotient uniform structure by means
of pseudometrics on the initial space. It is proved that if a uniform
structure on this space is subinvariant with respect to some given
set of its transformations then the quotient uniform structure is subinvariant
with respect to the induced transformations. The minimization for
a given family of pseudometrics is considered in the last section.
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Last modified: May 10, 2001