Ordinary Smooth Topological Spaces
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 t...
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| Published in | INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS Vol. 12; no. 1; pp. 66 - 76 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
한국지능시스템학회
2012
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1598-2645 2093-744X |
| DOI | 10.5391/IJFIS.2012.12.1.66 |
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| 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. |
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| AbstractList | 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. 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. KCI Citation Count: 4 |
| Author | Kul Hur Byeong Guk Ryoo Pyung Ki Lim |
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| Cites_doi | 10.1016/0165-0114(91)90100-5 10.1016/0165-0114(92)90329-3 10.1016/S0165-0114(98)00318-2 10.1016/0165-0114(92)90352-5 10.1016/0022-247X(80)90048-7 10.1016/0165-0114(93)90132-2 10.1016/0165-0114(93)90277-O 10.1016/0022-247X(68)90057-7 10.1016/0022-247X(76)90029-9 10.1016/0165-0114(92)90093-J |
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| Keywords | 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 |
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| Title | Ordinary Smooth Topological Spaces |
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