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On metrics of characteristic zero

Władysław Kulpa (2013)

Colloquium Mathematicae

We introduce and study the concept of characteristic for metrics. It turns out that metrizable spaces endowed with an L*-operator which admit a metric of characteristic zero play an important role in the theory of fixed points. We prove the existence of such spaces among infinite-dimensional linear topological spaces.

On Nash theorem

Władysław Kulpa, Andrzej Szymański (2002)

Acta Universitatis Carolinae. Mathematica et Physica

On relatively contractive relations in pairs of generalized uniform spaces.

Víctor M. Onieva Aleixandre, Javier Ruiz Fernández de Pinedo (1982)

Revista Matemática Hispanoamericana

J. C. Mathews and D. W. Curtis, [4], have introduced some structures which generalize structures of uniform types to the product of two sets, and they obtain a generalized version of Banach's contraction mapping theorem. In this note we prove that these structures are obtained from the usual analogues by means of a particular bijection; hence we do not have a meaningful generalization. For example, this bijection provides, from a result by A. S. Davies, [1], an analogue of Banach's well-known contraction...

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