Strong Cohomological Dimension
Volume 56 / 2008
Bulletin Polish Acad. Sci. Math. 56 (2008), 183-189
MSC: 55M10, 54F45.
DOI: 10.4064/ba56-2-9
Abstract
We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that $\mathop{\rm Ind}_G X = \dim_G X$ if $X$ is a separable metric ANR and $G$ is a countable Abelian group. Hence $\dim_{\mathbb{Z}} X = \dim X$ for any separable metric ANR $X$.
