Generalized closed maps. (English) Zbl 0578.54008

Malghan, S. R.

J. Karnatak Univ., Sci. 27, 82-88 (1982).

The author establishes the following theorems: (1) Normality is preserved under generalized-closed continuous surjections. (2) Regularity is preserved under generalized-closed continuous open surjections. (3) For any generalized-closed set A of a topological space X, Ind \(A\leq Ind X\) and dim \(A\leq \dim X\), where Ind and dim are large inductive dimensions and covering dimensions, respectively. These theorems are the natural extensions of the corresponding theorems for closed sets and closed functions.

Reviewer: E.Duda

MSC:

54C10	Special maps on topological spaces (open, closed, perfect, etc.)
54F45	Dimension theory in general topology

Keywords:

normality; generalized-closed continuous surjections; regularity; generalized-closed continuous open surjections; large inductive dimensions; covering dimensions