Abstract

NEIRA, CLARA MARINA  and  VARELA, JANUARIO. Localization with change of the base space in uniform bundles and sheaves. Rev.colomb.mat. [online]. 2007, vol.41, n.2, pp.303-323. ISSN 0034-7426.

In this paper a localization (germination) process with change of the base space is presented. The data consist of two topological spaces T and S, a continuous function φ:T\longrightarrow S, a surjective function p:E\longrightarrow T, a directed family (d_i)_{i\in I} of bounded pseudometrics for p generating a Hausdorff uniformity and a family Σ of global selections for p. In terms of these data, a uniform bundle is constructed over the base space S, whose fibers are colimits in a category of uniform spaces. Similar results follow for the case of sheaves of sets. This localization process leads to a universal arrow in a context described in terms of a category of uniform bundles.

Keywords : Uniform bundle; sheaf of sets; localization; colimit.

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