Displaying similar documents to “A theorem on expansions into inverse systems of metric spaces”

The category of uniform spaces as a completion of the category of metric spaces

Jiří Adámek, Jan Reiterman (1992)

Commentationes Mathematicae Universitatis Carolinae

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A criterion for the existence of an initial completion of a concrete category 𝐊 universal w.r.tḟinite products and subobjects is presented. For 𝐊 = metric spaces and uniformly continuous maps this completion is the category of uniform spaces.

Probabilistic approach spaces

Gunther Jäger (2017)

Mathematica Bohemica

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We study a probabilistic generalization of Lowen's approach spaces. Such a probabilistic approach space is defined in terms of a probabilistic distance which assigns to a point and a subset a distance distribution function. We give a suitable axiom scheme and show that the resulting category is isomorphic to the category of left-continuous probabilistic topological convergence spaces and hence is a topological category. We further show that the category of Lowen's approach spaces is...