- FUZZY P-LIMIT SPACES
- Min, Kyung-Chan ;
- Bulletin of the Korean Mathematical Society, volume 28, issue 2, 1991, Pages 191~199
Abstract
The notion of convergence in a fuzzy topological space was intorduced in various aspects as a local theory of fuzzy topologies [2,9,10,11,12,15,19,20]. In [12] a notion of fuzzy limitierung on a set is defined in terms of prefilters convergent to a fuzzy point and allows natural function structure in it. In this paper using fuzzy x-filters we introduce a notion of convergence to a point in a set, called a fuzzy p-limitierung, generalizing that of fuzzy neighborhood system introduced by Warren [18], which characterizes fuzzy topology. The notion of fuzzy p-limitierung enables us to form a convenient class containing all fuzzy topological spaces and all limit spaces. In section 4 we show that in fuzzy topology there is no natural function space structure. We show that fuzzy p-limit spaces form a quasitopos and give explicitly natural function space structure in it, providing an exponential law C(X*Y,Z)=C(X,C(Y,Z)). Form a categorical point of view the category FpLim of fuzzy p-limit spaces and fuzzy continuous maps is shown to be a quasitopos (=topological universe) containing the category FTop of fuzzy topological spaces as a bireflective subcategory and the category Lim of limit spaces as a bicoreflective subcategory. Throughout this paper, we use Lowen's notion of fuzzy topology[7]. For categorical background we refer to [4, 6]