Generalized ultrametric spaces: completion, topology, and powerdomains via the Yoneda embedding
Abstract: "Generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces (Lawvere 1973, Rutten 1995). Combining Lawvere's (1973) enriched-categorical and Smyth' [sic] (1987, 1991) topological view on generalized (ultra)metric spaces, it is sho...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
1995
|
| Series: | Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS
95,60 |
| Subjects: | |
| Summary: | Abstract: "Generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces (Lawvere 1973, Rutten 1995). Combining Lawvere's (1973) enriched-categorical and Smyth' [sic] (1987, 1991) topological view on generalized (ultra)metric spaces, it is shown how to construct 1. completion, 2. topology, and 3. powerdomains for generalized ultrametric spaces. Restricted to the special cases of preorders and ordinary ultrametric spaces, these constructions yield, respectively: 1. chain completion and Cauchy completion; 2. the Alexandroff and the Scott topology, and the [epsilon]-ball topology; 3. lower, upper, and convex powerdomains, and the powerdomain of compact subsets. Interestingly, all constructions are formulated in terms of (an ultrametric version of) the Yoneda (1954) lemma." |
| Physical Description: | 43 S. |
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MARC
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| 100 | 1 | |a Bonsangue, Marcello M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Generalized ultrametric spaces |b completion, topology, and powerdomains via the Yoneda embedding |c M. M. Bonsangue ; F. van Breugel ; J. J. M. M. Rutten |
| 264 | 1 | |a Amsterdam |c 1995 | |
| 300 | |a 43 S. | ||
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS |v 95,60 | |
| 520 | 3 | |a Abstract: "Generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces (Lawvere 1973, Rutten 1995). Combining Lawvere's (1973) enriched-categorical and Smyth' [sic] (1987, 1991) topological view on generalized (ultra)metric spaces, it is shown how to construct 1. completion, 2. topology, and 3. powerdomains for generalized ultrametric spaces. Restricted to the special cases of preorders and ordinary ultrametric spaces, these constructions yield, respectively: 1. chain completion and Cauchy completion; 2. the Alexandroff and the Scott topology, and the [epsilon]-ball topology; 3. lower, upper, and convex powerdomains, and the powerdomain of compact subsets. Interestingly, all constructions are formulated in terms of (an ultrametric version of) the Yoneda (1954) lemma." | |
| 650 | 4 | |a Metric spaces | |
| 650 | 4 | |a Set theory | |
| 700 | 1 | |a Breugel, Franck van |e Verfasser |4 aut | |
| 700 | 1 | |a Rutten, Jan J. |e Verfasser |4 aut | |
| 810 | 2 | |a Department of Computer Science: Report CS |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 95,60 |w (DE-604)BV008928356 |9 95,60 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007410633 | ||
Record in the Search Index
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| any_adam_object | |
| author | Bonsangue, Marcello M. Breugel, Franck van Rutten, Jan J. |
| author_facet | Bonsangue, Marcello M. Breugel, Franck van Rutten, Jan J. |
| author_role | aut aut aut |
| author_sort | Bonsangue, Marcello M. |
| author_variant | m m b mm mmb f v b fv fvb j j r jj jjr |
| building | Verbundindex |
| bvnumber | BV011064713 |
| ctrlnum | (OCoLC)35649302 (DE-599)BVBBV011064713 |
| format | Book |
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| id | DE-604.BV011064713 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:03:24Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007410633 |
| oclc_num | 35649302 |
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| physical | 43 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS |
| spelling | Bonsangue, Marcello M. Verfasser aut Generalized ultrametric spaces completion, topology, and powerdomains via the Yoneda embedding M. M. Bonsangue ; F. van Breugel ; J. J. M. M. Rutten Amsterdam 1995 43 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS 95,60 Abstract: "Generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces (Lawvere 1973, Rutten 1995). Combining Lawvere's (1973) enriched-categorical and Smyth' [sic] (1987, 1991) topological view on generalized (ultra)metric spaces, it is shown how to construct 1. completion, 2. topology, and 3. powerdomains for generalized ultrametric spaces. Restricted to the special cases of preorders and ordinary ultrametric spaces, these constructions yield, respectively: 1. chain completion and Cauchy completion; 2. the Alexandroff and the Scott topology, and the [epsilon]-ball topology; 3. lower, upper, and convex powerdomains, and the powerdomain of compact subsets. Interestingly, all constructions are formulated in terms of (an ultrametric version of) the Yoneda (1954) lemma." Metric spaces Set theory Breugel, Franck van Verfasser aut Rutten, Jan J. Verfasser aut Department of Computer Science: Report CS Centrum voor Wiskunde en Informatica <Amsterdam> 95,60 (DE-604)BV008928356 95,60 |
| spellingShingle | Bonsangue, Marcello M. Breugel, Franck van Rutten, Jan J. Generalized ultrametric spaces completion, topology, and powerdomains via the Yoneda embedding Metric spaces Set theory |
| title | Generalized ultrametric spaces completion, topology, and powerdomains via the Yoneda embedding |
| title_auth | Generalized ultrametric spaces completion, topology, and powerdomains via the Yoneda embedding |
| title_exact_search | Generalized ultrametric spaces completion, topology, and powerdomains via the Yoneda embedding |
| title_full | Generalized ultrametric spaces completion, topology, and powerdomains via the Yoneda embedding M. M. Bonsangue ; F. van Breugel ; J. J. M. M. Rutten |
| title_fullStr | Generalized ultrametric spaces completion, topology, and powerdomains via the Yoneda embedding M. M. Bonsangue ; F. van Breugel ; J. J. M. M. Rutten |
| title_full_unstemmed | Generalized ultrametric spaces completion, topology, and powerdomains via the Yoneda embedding M. M. Bonsangue ; F. van Breugel ; J. J. M. M. Rutten |
| title_short | Generalized ultrametric spaces |
| title_sort | generalized ultrametric spaces completion topology and powerdomains via the yoneda embedding |
| title_sub | completion, topology, and powerdomains via the Yoneda embedding |
| topic | Metric spaces Set theory |
| topic_facet | Metric spaces Set theory |
| volume_link | (DE-604)BV008928356 |
| work_keys_str_mv | AT bonsanguemarcellom generalizedultrametricspacescompletiontopologyandpowerdomainsviatheyonedaembedding AT breugelfranckvan generalizedultrametricspacescompletiontopologyandpowerdomainsviatheyonedaembedding AT ruttenjanj generalizedultrametricspacescompletiontopologyandpowerdomainsviatheyonedaembedding |