Regular relations and completely regular spaces. (Chinese. English summary) Zbl 1199.54138
Summary: The main purpose of this paper is to characterize the complete regularity of topological spaces by some algebraic properties of certain binary relations between closed subsets and open subsets. It is proved that a topological space is completely regular if and only if there are certain regular, finitely regular, or generalized finitely regular relations between closed subsets and open subsets.
MSC:
| 54D15 | Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) |
| 03E20 | Other classical set theory (including functions, relations, and set algebra) |
| 06B35 | Continuous lattices and posets, applications |
