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Given a Tychonoff space $X$ , a base $α$ for an ideal on $X$ is called pseudouniform if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on $α$ converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.

Quantifying completion.

Lowen, Robert, Windels, Bart (2000)

International Journal of Mathematics and Mathematical Sciences

Quasi-metrization and completion for Pervin's quasi-uniformity.

V. Gregori, J. Ferrer (1982)

Stochastica

R. Stoltenberg characterized in [2] those quasi-uniformities which are quasi-pseudometrizable, as well as those quasi-metric spaces which have a quasi-metric completion. In this paper we follow Stoltenberg's work by giving characterizations for quasi-metrizability and quasi-metric completion for a particular type of quasi-uniform spaces, the Pervin's quasi-uniform space.

Quasi-proximities for topological spaces.

W.J. PERVIN (1963)

Mathematische Annalen

Quasi-uniform completions of partially ordered spaces

David Buhagiar, Tanja Telenta (2007)

Mathematica Slovaca

Quasi-uniform Space

Roland Coghetto (2016)

Formalized Mathematics

In this article, using mostly Pervin [9], Kunzi [6], [8], [7], Williams [11] and Bourbaki [3] works, we formalize in Mizar [2] the notions of quasiuniform space, semi-uniform space and locally uniform space. We define the topology induced by a quasi-uniform space. Finally we formalize from the sets of the form ((X Ω) × X) ∪ (X × Ω), the Csaszar-Pervin quasi-uniform space induced by a topological space.