| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4659699 | Topology and its Applications | 2011 | 4 Pages |
Abstract
Let R denote the real numbers. We construct in ZFC a countable space X such that X has exactly one non-isolated point, X is infraconsonant, and X is not consonant. We conclude that X is a completely regular space such that Isbell topology on C(X,R) is a group topology that coincides with the natural (finest splitting) topology on C(X,R), but the Isbell and compact-open topologies on C(X,R) do not coincide. The example answers two open problems in the literature.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
