International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 7, Pages 387-399
doi:10.1155/S0161171202202203
Neighborhood spaces
D.C. Kent1
and Won Keun Min2
1Department of Mathematics, Washington State University, Pullman 99164-3113, WA, USA
2Department of Mathematics, Kangwon National University, Chuncheon 200-701, Korea
Abstract
Neighborhood spaces, pretopological spaces, and closure spaces are topological space generalizations which can be characterized by means of their associated interior (or closure) operators. The category NBD of neighborhood spaces and continuous maps contains PRTOP as a bicoreflective subcategory and CLS as a bireflective subcategory, whereas TOP is bireflectively embedded in PRTOP and bicoreflectively embedded in CLS. Initial and final structures are described in these categories, and it is shown that the Tychonov theorem holds in all of them. In order to describe a successful convergence theory in NBD, it is necessary to replace filters by more general p-stacks.