1Department of Mathematics University of Tennessee Knoxville, TN 37996, U.S.A. 2Department 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
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 $X$.
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
Affiliations des auteurs :
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
@article{10_4064_ba56_2_9,
author = {Jerzy Dydak and Akira Koyama},
title = {Strong {Cohomological} {Dimension}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {183--189},
year = {2008},
volume = {56},
number = {2},
doi = {10.4064/ba56-2-9},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba56-2-9/}
}
TY - JOUR
AU - Jerzy Dydak
AU - Akira Koyama
TI - Strong Cohomological Dimension
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2008
SP - 183
EP - 189
VL - 56
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4064/ba56-2-9/
DO - 10.4064/ba56-2-9
LA - en
ID - 10_4064_ba56_2_9
ER -
%0 Journal Article
%A Jerzy Dydak
%A Akira Koyama
%T Strong Cohomological Dimension
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2008
%P 183-189
%V 56
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/ba56-2-9/
%R 10.4064/ba56-2-9
%G en
%F 10_4064_ba56_2_9
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
