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http://dx.doi.org/10.5391/IJFIS.2012.12.1.66

Ordinary Smooth Topological Spaces  

Lim, Pyung-Ki (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
Ryoo, Byeong-Guk (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
Publication Information
International Journal of Fuzzy Logic and Intelligent Systems / v.12, no.1, 2012 , pp. 66-76 More about this Journal
Abstract
In this paper, we introduce the concept of ordinary smooth topology on a set X by considering the gradation of openness of ordinary subsets of X. And we obtain the result [Corollary 2.13] : An ordinary smooth topology is fully determined its decomposition in classical topologies. Also we introduce the notion of ordinary smooth [resp. strong and weak] continuity and study some its properties. Also we introduce the concepts of a base and a subbase in an ordinary smooth topological space and study their properties. Finally, we investigate some properties of an ordinary smooth subspace.
Keywords
ordinary smooth (co)topological space; r-level and strong r-level; ordinary smooth [resp. weak and strong] continuity; ordinary smooth open [resp. closed] mapping; ordinary smooth subspace; ordinary smooth base [resp. subbase];
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