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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2575-2578
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 α-expansion α-continuous, where 𝒜α, α are two mutually dual expansions.