Name
Abstract | ||
|---|---|---|
Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of T-0 spaces instead of restricting to posets. In this paper, we respond to this calling with an attempt to formulate a topological version of the Scott Convergence Theorem, i.e., an order-theoretic characterisation of those posets for which the Scott-convergence S is topological. To do this, we make use of the ID replacement principle to create topological analogues of well-known domain-theoretic concepts, e.g., I-continuous spaces correspond to continuous posets, as I-convergence corresponds to S-convergence. In this paper, we consider two novel topological concepts, namely, the I-stable spaces and the DI spaces, and as a result we obtain some necessary (respectively, sufficient) conditions under which the convergence structure I is topological. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.23638/LMCS-15(1:29)2019 | LOGICAL METHODS IN COMPUTER SCIENCE |
Keywords | Field | DocType |
Scott convergence,topological convergence,irreducibly derived topology,I-continuous spaces,I-stable spaces,DI spaces | Topological algebra,Discrete mathematics,Topology,Combinatorics,Compact convergence,Topological vector space,Dominated convergence theorem,Pointwise convergence,Unconditional convergence,Closed graph theorem,Mathematics,Modes of convergence | Journal |
Volume | Issue | ISSN |
15 | 1 | 1860-5974 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hadrian Andradi | 1 | 0 | 0.34 |
| Weng Kin Ho | 2 | 23 | 5.41 |