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Semi-generalized closed maps and generalized semi-closed maps. (English) Zbl 0787.54015

P. Sundaram [Ph.D. Thesis, Bharathian University Combatore (1991)] introduced the concept of semi-generalized continuous maps and generalized semi-continuous maps. In this paper the authors introduce semi-generalized closed maps and generalized semi-continuous closed maps and study some of their basic properties. They show for example that under a continuous generalized semi-continuous closed surjection the image of a normal space is \(s\)-normal and that under a semi-open continuous generalized semi-closed surjection the image of a regular space is \(s\)-regular. They also characterize the class of \(T_{1/2}\) spaces by using semi-closed sets and generalized semi-closed sets.

MSC:

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