International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 24, Pages 3909-3923
doi:10.1155/IJMMS.2005.3909
Equivalence among some neighborhood structures in fuzzy topology
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.
Abstract
We deepen the study of two known neighborhood structures, which
here will be called f⋅k-neighborhood structures and f⋅q-neighborhood structures, in the context of Šostak fuzzy
topological spaces. In particular, we characterize fuzzy
topologies by f⋅k-neighbor-hood structures. Moreover we introduce and discuss the notions of
f⋅k-neighborhood prestructure and f⋅m-neighborhood structure in the same context. At last we prove that the three
neighborhood structures mentioned above are equivalent.