International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3909-3923

Equivalence among some neighborhood structures in fuzzy topology

Cosimo De Mitri

Department of Mathematics “Ennio De Giorgi”, University of Lecce, via Arnesano, C.P. 193, Lecce 73100, Italy

Received 15 March 2005; Revised 26 October 2005

Copyright © 2005 Cosimo De Mitri. 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.


We deepen the study of two known neighborhood structures, which here will be called fk-neighborhood structures and fq-neighborhood structures, in the context of Šostak fuzzy topological spaces. In particular, we characterize fuzzy topologies by fk-neighbor-hood structures. Moreover we introduce and discuss the notions of fk-neighborhood prestructure and fm-neighborhood structure in the same context. At last we prove that the three neighborhood structures mentioned above are equivalent.