http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
The Rings Cκ(X) and C∞(X) -Some Remarks
S.K.Acharyya,K.C. Chattopadhyay,Partha PratimGhosh 경북대학교 자연과학대학 수학과 2003 Kyungpook mathematical journal Vol.43 No.3
Let X be a locally compact Hausdorff space and C1 (X ) be the ring of all real valued continuous functions on X which vanish at infinity. Suppose CK (X ) is the set of all real valued continuous functions on X which have compact support, then CK (X ) is a subring of C1 (X ). We have shown that every maximal ideal of C1 (X ) is fixed from which it follows that if CK (X ) 6= C1 (X ) then CK (X ) is a proper ideal of C1 (X ) which is not extendable to any maximal ideal. By using the same result we have further established that two, locally compact Hausdorff spaces X and Y are homeomorphic if and only if C1 (X ) and C1 (Y) (respectivelyCK (X ) and CK (Y)) are isomorphic.