International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 41, Pages 2609-2617

α-fuzzy compactness in I-topological spaces

Valentín Gregori1 and Hans-peter A. Künzi2

1Escuela Politécnica Superior de Gandía, Carretera Nazaret-Oliva s/n, Grao de Gandía 46730, Spain
2Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa

Received 28 April 2002

Copyright © 2003 Valentín Gregori and Hans-peter A. Künzi. 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.


Using a gradation of openness in a (Chang fuzzy) I-topological space, we introduce degrees of compactness that we call α-fuzzy compactness (where α belongs to the unit interval), so extending the concept of compactness due to C. L. Chang. We obtain a Baire category theorem for α-locally compact spaces and construct a one-point α-fuzzy compactification of an I-topological space.