International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2575-2578
doi:10.1155/IJMMS.2005.2575
Expansion of α-open sets and decomposition of α-continuous mappings
Post Graduate and Research Department of Mathematics, N.G.M. College (Autonomous), Bharathiar University, Coimbatore, Pollachi, Tamil Nadu 642 001, India
Received 6 November 2004; Revised 22 June 2005
Copyright © 2005 M. Rajamani and K. Bagyalakshmi. 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.
Abstract
We introduce the notions of expansion 𝒜α of α-open sets and 𝒜α-expansion
α-continuous mappings in topological spaces. The
main result of this paper is that a map f is α-continuous
if and only if it is 𝒜α-expansion
α-continuous and ℬα-expansion
α-continuous, where 𝒜α, ℬα are two mutually dual expansions.