Paper Info
Title
Ideal Completions and Compactifications
Abstract
The core of a point in a topological space is the intersection of its neighborhoods. We construct certain completions and compactifications for densely core-generated spaces, i.e., T0-spaces having a subbasis of open cores such that the points with open cores are dense in the associated patch space. All T0-spaces with a minimal basis are in that class. Densely core-generated spaces admit not only a coarsest quasi-uniformity (the unique totally bounded transitive compatible quasi-uniformity), but also a purely order-theoretical description by means of their specialization order and a suitable join-dense subset (join-basis). It turns out that the underlying ordered sets of the completions and compactifications obtained are, up to isomorphism, certain ideal completions of the join-basis. The topology of the resulting completion or compactification is the Lawson topology or the Scott topology, or a slight modification of these.
Year
DOI
Venue
2001
10.1023/A:1011260817824
Applied Categorical Structures
Keywords
Field
DocType
Cauchy filter,compactification,completion,core,ideal,(quasi-)uniform space,(ordered) topological space,(strongly) sober,totally (order-) separated
Trivial topology,Order topology,Discrete mathematics,Topology,Combinatorics,Topological space,Net (mathematics),General topology,Specialization (pre)order,Connected space,Filter (mathematics),Mathematics
Journal
Volume
Issue
ISSN
9
3
1572-9095
Citations 
PageRank 
References 
1
0.38
0
Authors
1
Name
Order
Citations
PageRank
Marcel Erné12910.77