International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 507-512
Department of Mathematics, East Central University, Ada 74820, Oklahoma, USA
Received 12 June 1989; Revised 4 December 1989
Copyright © 1990 T. R. Hamlett and David Rose. 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.
An ideal on a set is a nonempty collection of subsets of closed under the operations of subset (heredity) and finite unions (additivity). Given a topological space an ideal on and , is defined as . A topology, denoted , finer than is generated by the basis , and a topology, denoted , coarser than is generated by the basis . The notation denotes a topological space with an ideal on . A bijection is called a -homeomorphism if is a homeomorphism, and is called a -homeomorphism if is a homeomorphism. Properties preserved by -homeomorphisms are studied as well as necessary and sufficient conditions for a
-homeomorphism to be a -homeomorphism. The semi-homeomorphisms and semi-topological properties of Crossley and Hildebrand [Fund. Math., LXXIV (1972), 233-254] are shown to be special case.