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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...

On resolvable spaces and groups

Luis Miguel Villegas-Silva (1995)

Commentationes Mathematicae Universitatis Carolinae

It is proved that every uncountable ω -bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.

On Semicontinuity in Impulsive Dynamical Systems

Krzysztof Ciesielski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

In the important paper on impulsive systems [K1] several notions are introduced and several properties of these systems are shown. In particular, the function ϕ which describes "the time of reaching impulse points" is considered; this function has many important applications. In [K1] the continuity of this function is investigated. However, contrary to the theorem stated there, the function ϕ need not be continuous under the assumptions given in the theorem. Suitable examples are shown in this paper....

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