On semi-homeomorphisms
Summary: We show a condition for a semi-homeomorphism in the sense of \textit{S. G. Crossley} and \textit{S. K. Hildebrand} [Fundam. Math. 74, 233-254 (1972; Zbl 0206.515)] to be a semi-homeomorphism in the sense of \textit{N. Biswas} [``On some mappings in topological spaces, Thesis, Univ. of Calcutta (1971)]. Certain relevant examples are provided. Next, we define strong semi-homeomorphisms via ``nice'' restrictions of semi- homeomorphisms (``global condition'') and show that the new class of functions actually coincides with semi-homeomorphisms. Then we introduce local semi-homeomorphisms via a corresponding ``local condition'' for restrictions. A few results pertaining to the preservation of some topological properties under this new class of functions are examined.
scientific article; zbMATH DE number 4140778