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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2006.1
- 수록면
- 503 - 507 (5page)
이용수
초록· 키워드
오류제보하기
Let X be a Tychono�� space and P(X) the set of all the subrings of
C(X) that contain C¤(X). For any A(X) in P(X) suppose ÀAX is the largest subspace
of ¯X containing X to which each function in A(X) can be extended continuously.
Let us write A(X) » B(X) if and only if ÀAX = ÀBX, thereby defining an
equivalence relation on P(X). We have shown that an A(X) in P(X) is isomorphic
to C(Y ) for some space Y if and only if A(X) is the largest member of its equivalence
class if and only if there exists a subspace T of ¯X with the property that
A(X) = ff 2 C(X) : f¤(p) is real for each p in Tg, f¤ being the unique continuous extension
of f in C(X) from ¯X to R¤, the one point compactification of R. As a consequence
it follows that if X is a realcompact space in which every C¤-embedded subset is closed,
then C(X) is never isomorphic to any A(X) in P(X) without being equal to it.
목차
등록된 정보가 없습니다.
참고문헌 (6)
참고문헌 신청
/ 1961 / On the structure of a class of archimedean latticeordered algebras 50 : 73 ~ 94
/ 1969 / On a class of subalgebras of C with application to ？
/ 1976. / Rings of continuous functions
/ 1977 / Intermediate algebras between C？ as rings of fractions of C？ : 115 ~ 130
/ 1997 / On a class of subalgebrasof C and the intersection of their free maximal ideals 125 (2) : 611 ~ 615
/ 1969 / On a class of subalgebras of C with application to ？
/ 1976. / Rings of continuous functions
/ 1977 / Intermediate algebras between C？ as rings of fractions of C？ : 115 ~ 130
/ 1997 / On a class of subalgebrasof C and the intersection of their free maximal ideals 125 (2) : 611 ~ 615
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