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On relatively contractive relations in pairs of generalized uniform spaces.

Víctor M. Onieva AleixandreJavier 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...

Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series

Francisco Javier Pérez FernándezF. Benítez-TrujilloAntonio Aizpuru Tomás — 2000

Czechoslovak Mathematical Journal

In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space X can be characterized through the behaviour of its weakly- * unconditionally Cauchy series in X * .

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