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Displaying similar documents to “Ekeland's principle for vector-valued maps based on the characterization of uniform spaces via families of generalized quasi-metrics.”

Quasi-uniform Space

Roland Coghetto (2016)

Formalized Mathematics

Similarity:

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.

On half-completion and bicompletion of quasi-metric spaces

Elena Alemany, Salvador Romaguera (1996)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We characterize the quasi-metric spaces which have a quasi-metric half-completion and deduce that each paracompact co-stable quasi-metric space having a quasi-metric half-completion is metrizable. We also characterize the quasi-metric spaces whose bicompletion is quasi-metric and it is shown that the bicompletion of each quasi-metric compatible with a quasi-metrizable space X is quasi-metric if and only if X is finite.