## Generalized closed maps.(English)Zbl 0578.54008

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