ON THE FAILURE OF THE URYSOHN-MENGER SUM FORMULA FOR COHOMOLOGICAL DIMENSION

被引：9

作者：

DRANISNIKOV, AN ^{[1
]}

REPOVS, D ^{[1
]}

SCEPIN, EV ^{[1
]}

机构：

[1] VA STEKLOV MATH INST,MOSCOW 117966,RUSSIA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 120卷 / 04期

关键词：

URYSOHN-MENGER SUM FORMULA; COHOMOLOGICAL DIMENSION; BOLTYANSKII COMPACTA; BOCKSTEIN INEQUALITIES; DIMENSION TYPE; COMPACTIFICATION; COMPLETION;

D O I：

10.2307/2160247

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the classical Urysohn-Menger sum formula, dim(A or B) less-than-or-equal-to dim A + dim B + 1, which is also known to be true for co-homological dimension over the integers (and some other abelian groups), does not hold for cohomological dimension over an arbitrary abelian group of coefficients. In particular, we prove that there exist subsets A , B subset-of R4 such that 4 = dim(Q/Z)(A or B) > dim(Q/z) A + dim(Q/z) B + 1 = 3.

引用

页码：1267 / 1270

页数：4