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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-2-4,
author = {V. V. Fedorchuk},
title = {Inductive dimensions modulo simplicial complexes and ANR-compacta},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {223-247},
zbl = {1222.54035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-2-4}
}
V. V. Fedorchuk. Inductive dimensions modulo simplicial complexes and ANR-compacta. Colloquium Mathematicae, Tome 120 (2010) pp. 223-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm120-2-4/