Geodesic
Strong Cohomological Dimension
Jerzy Dydak 1   ; Akira Koyama 2
1 Department of Mathematics University of Tennessee Knoxville, TN 37996, U.S.A.
2 Department of Mathematics Faculty of Sciences Shizuoka University Oya 836, Shizuoka 422-8529, Japan
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 2, pp. 183-189 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $X$.
DOI : 10.4064/ba56-2-9
Keywords: characterize strong cohomological dimension separable metric spaces terms extension mappings using characterization discuss relation between strong cohomological dimension ordinal cohomological dimension examples clarify their gaps mathop ind dim separable metric anr countable abelian group hence dim mathbb dim separable metric anr

Jerzy Dydak  1   ; Akira Koyama  2

1 Department of Mathematics University of Tennessee Knoxville, TN 37996, U.S.A.
2 Department of Mathematics Faculty of Sciences Shizuoka University Oya 836, Shizuoka 422-8529, Japan 
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Jerzy Dydak; Akira Koyama. Strong Cohomological Dimension. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 2, pp. 183-189. doi: 10.4064/ba56-2-9

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