A Note on the T₁Space and Derived Set
 Alternative Title
 T₁空間과 導集合에 관한 小考
 Abstract
 位相空間 X가 T₁space라 함은 X의 각 한 점으로 구성된 집합들이 모두 closed일 때를 말하고. 한 set의 모든 集積點들의 집합을 導集合이라 부르기로 한다.
우리는 여기서 다음과 같은 사실을 밝힌다. 즉 만약 X가 T₁空間이면 X의 각 부분집합의 導集合은 closed이지만 그 逆은 성립하지 않으며 더욱 나아가서 어떤 空間 X의 각 부분집합의 3導集合이 closed일 필요하고도 충분한 조건은 X의 모든 singleton{x}의 導集合이 각각 closed인 것이다.
A topological space is a T₁space iff each set which consists of a single point is closed, and the set of all limit points of a set is called the derived set of it.
We show the following: If X is a T₁space then the derived set of each subset of X is closed, but the converse is not always true. Furthermore, as a sharper result, a necessary and sufficient condition that the derived set of each subset be closed is that the derived set of the singleton{x} be closed for each point x in a topological space X.
A topological space is a T₁space iff each set which consists of a single point is closed, and the set of all limit points of a set is called the derived set of it.
We show the following: If X is a T₁space then the derived set of each subset of X is closed, but the converse is not always true. Furthermore, as a sharper result, a necessary and sufficient condition that the derived set of each subset be closed is that the derived set of the singleton{x} be closed for each point x in a topological space X.
 Author(s)
 Lee, Kwang Young
 Issued Date
 1974
 Type
 Research Laboratory
 URI
 https://oak.ulsan.ac.kr/handle/2021.oak/4892
http://ulsan.dcollection.net/jsp/common/DcLoOrgPer.jsp?sItemId=000002025178
 Alternative Author(s)
 이광영
 Publisher
 연구논문집
 Language
 eng
 Rights
 울산대학교 저작물은 저작권에 의해 보호받습니다.
 Citation Volume
 5
 Citation Number
 1
 Citation Start Page
 57
 Citation End Page
 60

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