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On extended frames

Jorge Picado (1995)

Commentationes Mathematicae Universitatis Carolinae

Some aspects of extended frames are studied, namely, the behaviour of ideals, covers, admissible systems of covers and uniformities.

On finest unitary extensions of topological monoids

Boris G. Averbukh (2015)

Topological Algebra and its Applications

We prove that the Wyler completion of the unitary Cauchy space on a given Hausdorff topological 5 monoid consisting of the underlying set of this monoid and of the family of unitary Cauchy filters on it, is a T2-topological space and, in the commutative case, an abstract monoid containing the initial one.

On half-completion and bicompletion of quasi-metric spaces

Elena Alemany, Salvador Romaguera (1996)

Commentationes Mathematicae Universitatis Carolinae

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.

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