Details
| Original language | English |
|---|---|
| Pages (from-to) | 471-496 |
| Number of pages | 26 |
| Journal | Applied categorical structures |
| Volume | 24 |
| Issue number | 5 |
| Publication status | Published - 19 Aug 2016 |
Abstract
A basic tool in domain theory and point-free topology are (Scott) open filters in a partially ordered set. A systematic investigation of that concept shows that central notions and facts like Lawson’s famous self-duality of the category of continuous domains may be established without invoking any choice principles, if only continuous domains are replaced by so-called δ-domains, which coincide with the former in the presence of dependent choices. Many of the conclusions remain valid for the more flexible notion of ζ-domains, comprising important variants such as algebraic or hypercontinuous domains.
Keywords
- (ζ-) basis, (ζ-) continuous, (ζ-) domain, Algebraic, Choice principle, Compact, Duality, Open filter, Supercompact, Supercontinuous
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Computer Science(all)
- General Computer Science
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In: Applied categorical structures, Vol. 24, No. 5, 19.08.2016, p. 471-496.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Choice-Free Dualities for Domains
AU - Erné, Marcel
PY - 2016/8/19
Y1 - 2016/8/19
N2 - A basic tool in domain theory and point-free topology are (Scott) open filters in a partially ordered set. A systematic investigation of that concept shows that central notions and facts like Lawson’s famous self-duality of the category of continuous domains may be established without invoking any choice principles, if only continuous domains are replaced by so-called δ-domains, which coincide with the former in the presence of dependent choices. Many of the conclusions remain valid for the more flexible notion of ζ-domains, comprising important variants such as algebraic or hypercontinuous domains.
AB - A basic tool in domain theory and point-free topology are (Scott) open filters in a partially ordered set. A systematic investigation of that concept shows that central notions and facts like Lawson’s famous self-duality of the category of continuous domains may be established without invoking any choice principles, if only continuous domains are replaced by so-called δ-domains, which coincide with the former in the presence of dependent choices. Many of the conclusions remain valid for the more flexible notion of ζ-domains, comprising important variants such as algebraic or hypercontinuous domains.
KW - (ζ-) basis
KW - (ζ-) continuous
KW - (ζ-) domain
KW - Algebraic
KW - Choice principle
KW - Compact
KW - Duality
KW - Open filter
KW - Supercompact
KW - Supercontinuous
UR - http://www.scopus.com/inward/record.url?scp=84982299364&partnerID=8YFLogxK
U2 - 10.1007/s10485-016-9444-0
DO - 10.1007/s10485-016-9444-0
M3 - Article
AN - SCOPUS:84982299364
VL - 24
SP - 471
EP - 496
JO - Applied categorical structures
JF - Applied categorical structures
SN - 0927-2852
IS - 5
ER -