Name
Abstract | ||
|---|---|---|
We provide the appropriate common ‘(pre)framework’ for various central results of domain theory and topology, like the Lawson
duality of continuous domains, the Hofmann–Lawson duality between continuous frames and locally compact sober spaces, the
Hofmann–Mislove theorems about continuous semilattices of compact saturated sets, or the theory of stably continuous frames
and their topological manifestations. Suitable objects for the pointfree approach are quasiframes, i.e., up-complete meet-semilattices
with top, and preframes, i.e., meet-continuous quasiframes. We introduce the pointfree notion of locally compact well-filtered
preframes, show that they are just the continuous preframes (using a slightly modified definition of continuity) and establish
several natural dualities for the involved categories. Moreover, we obtain various characterizations of preframes having duality.
Our results hold in ZF set theory without any choice principles. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s10485-006-9029-4 | Applied Categorical Structures |
Keywords | Field | DocType |
domain,duality,open filter,locally compact,preframe,quasiframe,saturated,sober,spatial,well-filtered,Primary 06B35,Secondary 03E25,18B30,54D45 | Set theory,Discrete mathematics,Topology,Locally compact space,Algebra,Weak duality,Duality (mathematics),Domain theory,Duality (optimization),Stone duality,Mathematics | Journal |
Volume | Issue | ISSN |
15 | 5-6 | 1572-9095 |
Citations | PageRank | References |
3 | 1.74 | 0 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcel Erné | 1 | 29 | 10.77 |