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Weak completeness of the Bourbaki quasi-uniformity
dc.contributor.author | Sánchez-Granero, M.A | |
dc.date.accessioned | 2017-06-16T08:23:39Z | |
dc.date.available | 2017-06-16T08:23:39Z | |
dc.date.issued | 2001 | |
dc.identifier.uri | http://hdl.handle.net/10835/4862 | |
dc.description.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. | es_ES |
dc.language.iso | en | es_ES |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.title | Weak completeness of the Bourbaki quasi-uniformity | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |
dc.identifier.doi | https://doi.org/10.4995/agt.2001.3018 |