Weak completeness of the Bourbaki quasi-uniformity
<p>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.</p>
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1995 ◽
Vol 173
(1)
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pp. 287-295
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1977 ◽
Vol 80
(5)
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pp. 353-356
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1974 ◽
Vol 55
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pp. 45-54
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1993 ◽
Vol 56
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pp. 297-301
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1956 ◽
Vol 52
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pp. 399-405
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