한국수학사학회지 (Journal for History of Mathematics)
- 제18권4호
- /
- Pages.113-124
- /
- 2005
- /
- 1226-931X(pISSN)
Quasi-F 공간과 극소 Quasi-F cover의 역사적 배경
Historical backgrounds of Quasi-F spaces and minimal quasi-F covers
- 김창일 (단국대학교 수학교육학과)
- Kim, Chang-Il (Department of Mathematics Educations, Dankook University)
- 발행 : 2005.11.01
초록
티코노프공간 X에 대하여 C(X)와
For a Tychonoff space X, C(X) is a Riesz-space. It is well known that C(X) is order-Cauchy complete if and only if X is a quasi~F space and that if X is a compact space and QF(X) is a minimal quasi-F cover of X, then the order- Cauchy completion of C(X) is isomorphic to C(QF(X)). In this paper, we investigate motivations and historical backgrounds of the definition for quasi-spaces and the construction for minimal quasi-F covers.