A characterization of c-type subrings of C(X) of some kind

被引：0
|
作者：
Mitra, Biswajit [1 ]
Chowdhury, Debojyoti [1 ]
机构：
[1] Univ Burdwan, Dept Math, Bardhaman 713104, W Bengal, India
来源：
POSITIVITY | 2020年 / 24卷 / 05期
关键词：
Rings of continuous function; c-type rings; Uniform structure; Uniform completion; Galois correspondences; RINGS;
D O I：
10.1007/s11117-019-00724-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A commutative ring with unity is of a c-type if it is (ring) isomorphic with C(X) for some space X. In this paper, we have described a structural representation of c-type subrings of C(X) that separates points and contains the constant function 1, but not necessarily containing C*(X). It would be complete if all c-type subring of C(X) separate points and contains 1. But, we have produced an example of c-type ring which does not separate points. We have also produced an example of a subring of C(R) not containing C*(R) which is of c-type, R real line.
引用
收藏
页码：1181 / 1190
页数：10
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