International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 129-134

On semi-homeomorphisms

J. P. Lee

Department of Mathematics, State University of New York, College at Old Westbury, Old Westbury 11568, New York, USA

Received 5 May 1989; Revised 7 July 1989

Copyright © 1990 J. P. Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the first part of our work we show a condition for a semi-homeomorphism in the sense of Crossley and Hildebrand (s.h.C.H) to be a semi-homeomorphism in the sense of Biswas (s.h.B). Certain relevant examples are provided. Next, we define strong semi-homeomorphisms Via “nice” restrictions of semi-homeomorphisms (“global condition”) and we show that the new class of functions actually coincides with semi-homeomorphisms. Then, in the third part we introduce local semi-homeomorphisms (l.s.h.C.H.) 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.