Dedekind-MacNeille and related completions: subfitness, regularity, and Booleanness
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913785193693184 |
|---|---|
| author | Bezhanishvili, G. Dashiell Jr, F. Moshier, M. A. Walters-Wayland, J. |
| author_facet | Bezhanishvili, G. Dashiell Jr, F. Moshier, M. A. Walters-Wayland, J. |
| contents | Completions play an important rôle for studying structure by supplying elements that in some sense ``ought to be." Among these, the Dedekind-MacNeille completion is of particular importance. In 1968 Janowitz provided necessary and sufficient conditions for it to be subfit or Boolean. Another natural separation axiom connected to these is regularity. We explore similar characterizations of when closely related completions are subfit, regular, or Boolean. We are mainly interested in the Bruns-Lakser, ideal, and canonical completions, which (unlike the Dedekind-MacNeille completion) satisfy stronger forms of distributivity. The first two are widely used in pointfree topology, while the latter is of crucial importance in the semantics of modal logic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19171 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dedekind-MacNeille and related completions: subfitness, regularity, and Booleanness Bezhanishvili, G. Dashiell Jr, F. Moshier, M. A. Walters-Wayland, J. General Topology 54D10, 18F70, 06D22, 06B23, 06B15, 06D50, 06E15 Completions play an important rôle for studying structure by supplying elements that in some sense ``ought to be." Among these, the Dedekind-MacNeille completion is of particular importance. In 1968 Janowitz provided necessary and sufficient conditions for it to be subfit or Boolean. Another natural separation axiom connected to these is regularity. We explore similar characterizations of when closely related completions are subfit, regular, or Boolean. We are mainly interested in the Bruns-Lakser, ideal, and canonical completions, which (unlike the Dedekind-MacNeille completion) satisfy stronger forms of distributivity. The first two are widely used in pointfree topology, while the latter is of crucial importance in the semantics of modal logic. |
| title | Dedekind-MacNeille and related completions: subfitness, regularity, and Booleanness |
| topic | General Topology 54D10, 18F70, 06D22, 06B23, 06B15, 06D50, 06E15 |
| url | https://arxiv.org/abs/2405.19171 |