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.


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