## On feebly closed mappings.(English)Zbl 0604.54012

The concept of an open set gives rise to a variety of related concepts and the authors consider four of them: $$\alpha$$-set, semi-open set, preopen set, feebly open set. Each has its ”closed” counterpart and so one can consider mappings which are $$\alpha$$-closed, semi-closed, preclosed, feebly closed ($$\alpha$$-closed means that images of closed sets are $$\alpha$$-closed etc.). It seems that the main result of the paper is that $$\alpha$$-closed mappings coincide with the feebly closed ones and the authors proceed to investigate a little that class. The proofs are immediate and the examples simple.

### MSC:

 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54A05 Topological spaces and generalizations (closure spaces, etc.)

### Keywords:

$$\alpha$$-set; semi-open set; preopen set; feebly open set