Strong Cohomological Dimension

Jerzy Dydak, and Akira Koyama. "Strong Cohomological Dimension." Bulletin of the Polish Academy of Sciences. Mathematics 56.2 (2008): 183-189. <http://eudml.org/doc/281141>.

@article{JerzyDydak2008,
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 $Ind_\{G\} X = dim_\{G\} X$ if X is a separable metric ANR and G is a countable Abelian group. Hence $dim_\{ℤ\} X = dim X$ for any separable metric ANR X.},
author = {Jerzy Dydak, Akira Koyama},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {absolute extensor; cohomological dimension; dimension; strong cohomological dimension; generalized Eilenberg-Borsuk theorem; separable metrizable space},
language = {eng},
number = {2},
pages = {183-189},
title = {Strong Cohomological Dimension},
url = {http://eudml.org/doc/281141},
volume = {56},
year = {2008},
}

TY - JOUR
AU - Jerzy Dydak
AU - Akira Koyama
TI - Strong Cohomological Dimension
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2008
VL - 56
IS - 2
SP - 183
EP - 189
AB - 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 $Ind_{G} X = dim_{G} X$ if X is a separable metric ANR and G is a countable Abelian group. Hence $dim_{ℤ} X = dim X$ for any separable metric ANR X.
LA - eng
KW - absolute extensor; cohomological dimension; dimension; strong cohomological dimension; generalized Eilenberg-Borsuk theorem; separable metrizable space
UR - http://eudml.org/doc/281141
ER -