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 mapping theorem which trivially implies the main result of [4].
@article{urn:eudml:doc:39820,
title = {On relatively contractive relations in pairs of generalized uniform spaces. },
journal = {Revista Matem\'atica Hispanoamericana},
volume = {42},
year = {1982},
pages = {194-200},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39820}
}
Onieva Aleixandre, Víctor M.; Ruiz Fernández de Pinedo, Javier. On relatively contractive relations in pairs of generalized uniform spaces. . Revista Matemática Hispanoamericana, Tome 42 (1982) pp. 194-200. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39820/