Weak completeness of the Bourbaki quasi-uniformity
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 st...
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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2017
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| Online Access: | http://hdl.handle.net/10835/4862 https://doi.org/10.4995/agt.2001.3018 |
| _version_ | 1789406621846208512 |
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| author | Sánchez-Granero, M.A |
| author_facet | Sánchez-Granero, M.A |
| author_sort | Sánchez-Granero, M.A |
| collection | DSpace |
| description | 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. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-4862 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2017 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-48622023-04-12T19:40:19Z Weak completeness of the Bourbaki quasi-uniformity Sánchez-Granero, M.A 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. 2017-06-16T08:23:39Z 2017-06-16T08:23:39Z 2001 info:eu-repo/semantics/article http://hdl.handle.net/10835/4862 https://doi.org/10.4995/agt.2001.3018 en Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
| spellingShingle | Sánchez-Granero, M.A Weak completeness of the Bourbaki quasi-uniformity |
| title | Weak completeness of the Bourbaki quasi-uniformity |
| title_full | Weak completeness of the Bourbaki quasi-uniformity |
| title_fullStr | Weak completeness of the Bourbaki quasi-uniformity |
| title_full_unstemmed | Weak completeness of the Bourbaki quasi-uniformity |
| title_short | Weak completeness of the Bourbaki quasi-uniformity |
| title_sort | weak completeness of the bourbaki quasi-uniformity |
| url | http://hdl.handle.net/10835/4862 https://doi.org/10.4995/agt.2001.3018 |
| work_keys_str_mv | AT sanchezgraneroma weakcompletenessofthebourbakiquasiuniformity |