On large cohomological dimension and tautness

Journal of the Australian Mathematical Society

Satya Deo¹ 

[1] Subhash Muttepawar

关键词: primary 54 F 45;    secondary 55 N 30;    55 N 05;    54 D 50;   

DOI  :  10.1017/S1446788700022345

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We prove that for a non-discrete space X, the inequality DimL(X) ≥ dimL(X) + 1 always holds if (i) X is paracompact and each point is Gδ, or (ii) X is a completely paracompact Morita k-space. Consequently, if X is a non-discrete completely paracompact space in which each point is a Gδ-set or it is also a Morita k-space then, the equality DimL(X) = dimL(X) + 1 always holds. We apply this equality to show that for such a space X there exists a point x ∈ X and a family ϕ of supports on X such that {x} is not ϕ-taut with respect to sheaf cohomology. This generalizes a corresponding known result for Rn. We also discuss the usual sum theorems for this large cohomological dimension; the finite sum theorem for closed sets is proved, and for all others, counter examples are given. Subject to a small modification, however, all of the sum theorems hold for a large class of spaces.

【 授权许可】

Unknown