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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |