Endpoints in T0-Quasimetric Spaces: Part II
We continue our work on endpoints and startpoints in T0-quasimetric spaces. In particular we specialize some of our earlier results to the case of two-valued T0-quasimetrics, that is, essentially, to partial orders. For instance, we observe that in a complete lattice the startpoints (resp., endpoint...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/539573 |
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| author | Collins Amburo Agyingi Paulus Haihambo Hans-Peter A. Künzi |
| author_facet | Collins Amburo Agyingi Paulus Haihambo Hans-Peter A. Künzi |
| author_sort | Collins Amburo Agyingi |
| collection | DOAJ |
| description | We continue our work on endpoints and startpoints in
T0-quasimetric spaces. In particular we specialize some of our
earlier results to the case of two-valued T0-quasimetrics,
that is, essentially, to partial orders. For instance, we observe
that in a complete lattice the startpoints (resp., endpoints) in
our sense are exactly the completely join-irreducible (resp.,
completely meet-irreducible) elements. We also discuss for a
partially ordered set the connection between its
Dedekind-MacNeille completion and the q-hyperconvex hull of its
natural T0-quasimetric space. |
| format | Article |
| id | doaj-art-297a92203db34cb78c9767b8fccc7ee5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-297a92203db34cb78c9767b8fccc7ee52025-02-03T06:01:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/539573539573Endpoints in T0-Quasimetric Spaces: Part IICollins Amburo Agyingi0Paulus Haihambo1Hans-Peter A. Künzi2Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South AfricaDepartment of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South AfricaDepartment of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South AfricaWe continue our work on endpoints and startpoints in T0-quasimetric spaces. In particular we specialize some of our earlier results to the case of two-valued T0-quasimetrics, that is, essentially, to partial orders. For instance, we observe that in a complete lattice the startpoints (resp., endpoints) in our sense are exactly the completely join-irreducible (resp., completely meet-irreducible) elements. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and the q-hyperconvex hull of its natural T0-quasimetric space.http://dx.doi.org/10.1155/2013/539573 |
| spellingShingle | Collins Amburo Agyingi Paulus Haihambo Hans-Peter A. Künzi Endpoints in T0-Quasimetric Spaces: Part II Abstract and Applied Analysis |
| title | Endpoints in T0-Quasimetric Spaces: Part II |
| title_full | Endpoints in T0-Quasimetric Spaces: Part II |
| title_fullStr | Endpoints in T0-Quasimetric Spaces: Part II |
| title_full_unstemmed | Endpoints in T0-Quasimetric Spaces: Part II |
| title_short | Endpoints in T0-Quasimetric Spaces: Part II |
| title_sort | endpoints in t0 quasimetric spaces part ii |
| url | http://dx.doi.org/10.1155/2013/539573 |
| work_keys_str_mv | AT collinsamburoagyingi endpointsint0quasimetricspacespartii AT paulushaihambo endpointsint0quasimetricspacespartii AT hanspeterakunzi endpointsint0quasimetricspacespartii |