Authors
Citation
An. Dranisnikov et al., ON THE FAILURE OF THE URYSOHN-MENGER SUM FORMULA FOR COHOMOLOGICAL DIMENSION, Proceedings of the American Mathematical Society, 120(4), 1994, pp. 1267-1270
Citations number
14
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
ISSN journal
00029939
Volume
120
Issue
4
Year of publication
1994
Pages
1267 - 1270
Database
ISI
SICI code
0002-9939(1994)120:4<1267:OTFOTU>2.0.ZU;2-W
Abstract
We prove that the classical Urysohn-Menger sum formula, dim(A or B) le
ss-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 exis
t 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.