Ordinary Smooth Topological Spaces

• Published in: INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS Vol. 12; no. 1; pp. 66 - 76
• Main Authors: Lim, Pyung-Ki, Ryoo, Byeong-Guk, Hur, Kul
• Format: Journal Article
• Language: English
• Published: 한국지능시스템학회 2012
• Subjects: 전기공학; ordinary smooth open [resp. closed] mapping; ordinary smooth (co)topological space; ordinary smooth subspace; ordinary smooth base [resp. subbase]; r-level and strong r-level; ordinary smooth [resp. weak and strong] continuity; ordinary smooth open [resp; ordinary smooth base [resp; subbase; weak and strong] continuity; ordinary smooth [resp; closed] mapping
• ISSN: 1598-2645; 2093-744X
• DOI: 10.5391/IJFIS.2012.12.1.66

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.