Inductive dimensions modulo simplicial complexes and ANR-compacta

@article{V2010,
abstract = {We introduce and investigate inductive dimensions 𝒦 -Ind and ℒ-Ind for classes 𝒦 of finite simplicial complexes and classes ℒ of ANR-compacta (if 𝒦 consists of the 0-sphere only, then the 𝒦 -Ind dimension is identical with the classical large inductive dimension Ind). We compare K-Ind to K-Ind introduced by the author [Mat. Vesnik 61 (2009)]. In particular, for every complex K such that K * K is non-contractible, we construct a compact Hausdorff space X with K-Ind X not equal to K-dim X.},
author = {V. V. Fedorchuk},
journal = {Colloquium Mathematicae},
keywords = {dimension; inductive dimension; simplicial complex; -compactum; join},
language = {eng},
number = {2},
pages = {223-247},
title = {Inductive dimensions modulo simplicial complexes and ANR-compacta},
url = {http://eudml.org/doc/283837},
volume = {120},
year = {2010},
}

TY - JOUR
AU - V. V. Fedorchuk
TI - Inductive dimensions modulo simplicial complexes and ANR-compacta
JO - Colloquium Mathematicae
PY - 2010
VL - 120
IS - 2
SP - 223
EP - 247
AB - We introduce and investigate inductive dimensions 𝒦 -Ind and ℒ-Ind for classes 𝒦 of finite simplicial complexes and classes ℒ of ANR-compacta (if 𝒦 consists of the 0-sphere only, then the 𝒦 -Ind dimension is identical with the classical large inductive dimension Ind). We compare K-Ind to K-Ind introduced by the author [Mat. Vesnik 61 (2009)]. In particular, for every complex K such that K * K is non-contractible, we construct a compact Hausdorff space X with K-Ind X not equal to K-dim X.
LA - eng
KW - dimension; inductive dimension; simplicial complex; -compactum; join
UR - http://eudml.org/doc/283837
ER -