Weak completeness of the Bourbaki quasi-uniformity

Authors

  • M.A. Sánchez Granero Universidad de Almería

DOI:

https://doi.org/10.4995/agt.2001.3018

Keywords:

Bourbaki quasi-uniformity, Hausdorff quasi-uniformity, Half-completeness

Abstract

The concept of semicompleteness (weaker than half-completeness) is defined for the Bourbaki quasi-uniformity of the hyperspace of a quasi-uniform space. It is proved that the Bourbaki quasi-uniformity is semicomplete in the space of nonempty sets of a quasi-uniform space (X,U) if and only if each stable filter on (X,U*) has a cluster point in (X,U). As a consequence the space of nonempty sets of a quasi-pseudometric space is semicomplete if and only if the space itself is half-complete. It is also given a characterization of semicompleteness of the space of nonempty U*-compact sets of a quasi-uniform space (X,U) which extends the well known Zenor-Morita theorem.

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Author Biography

M.A. Sánchez Granero, Universidad de Almería

Área de Geometría y Topología

Facultad de Ciencias

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Published

2001-04-01

How to Cite

[1]
M. Sánchez Granero, “Weak completeness of the Bourbaki quasi-uniformity”, Appl. Gen. Topol., vol. 2, no. 1, pp. 101–112, Apr. 2001.

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