A unified view of (complete) regularity and certain variants of (complete) regularity.

*(English)*Zbl 0553.54006Given a topological property P which certain subsets of a topological space can have, the notions of a P-regular space, weakly P-regular space, completely P-regular space, and semilocally P-space are introduced. It is pointed out that many (more or less) well known regularity concepts in the literature are covered by these definitions if P varies. A few theorems concerning the preservation of these properties under certain mappings can be proved in this general context; each of them contains known results as special cases.

Reviewer’s remark: The notions of a strongly closed \(G_{\delta}\)-set and of a D-closed set which appear as item 13 respectively 14 in the table are identical.

Reviewer’s remark: The notions of a strongly closed \(G_{\delta}\)-set and of a D-closed set which appear as item 13 respectively 14 in the table are identical.

Reviewer: H.Brandenburg

##### MSC:

54D15 | Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) |

54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |