Name
Abstract | ||
|---|---|---|
Abstract. From the work of Simmons about nuclei in frames it follows that a topological space X is scattered if and only if each congruence on the frame of open sets is induced by a unique sub-space A so that = f(U; V ) j U \ A = V \ Ag, and that the same holds without the uniqueness requirement i X is weakly scattered (corrupt). We prove a seemingly similar but substantially di erent result about quasidiscrete topologies (in which arbitrary intersec-tions of open sets are open): each complete congruence on such a topology is induced by a subspace if and only if the correspond-ing poset is (order) scattered, i. e. contains no dense chain. More questions concerning relations between frame, complete, spatial, induced and open congruences are discussed as well. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1007/s10485-006-9054-3 | Applied Categorical Structures |
Keywords | Field | DocType |
Alexandroff topology,(complete) congruence,frame,quasidiscrete,scattered,spatial,superalgebraic,supercontinuous,Primary 06D10. Secondary 06A15,06D22,08A30,54H10 | Discrete mathematics,Topology,Uniqueness,Combinatorics,Topological space,Lattice (order),Subspace topology,Congruence relation,Congruence (geometry),Mathematics,Partially ordered set,Open set | Journal |
Volume | Issue | ISSN |
15 | 1-2 | 0927-2852 |
Citations | PageRank | References |
3 | 0.54 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcel Erné | 1 | 29 | 10.77 |
| Mai Gehrke | 2 | 349 | 49.19 |
| Ales Pultr | 3 | 72 | 24.12 |