# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## Strong Cohomological Dimension

### Tom 56 / 2008

Bulletin Polish Acad. Sci. Math. 56 (2008), 183-189 MSC: 55M10, 54F45. DOI: 10.4064/ba56-2-9

#### Streszczenie

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 $X$.

#### Autorzy

• Jerzy DydakDepartment of Mathematics
University of Tennessee
Knoxville, TN 37996, U.S.A.
e-mail