Extraordinary dimension theories generated by complexes
一般拓扑
2007-05-23 v1
摘要
We study the extraordinary dimension function dim_{L} introduced by \v{S}\v{c}epin. An axiomatic characterization of this dimension function is obtained. We also introduce inductive dimensions ind_{L} and Ind_{L} and prove that for separable metrizable spaces all three coincide. Several results such as characterization of dim_{L} in terms of partitions and in terms of mappings into -dimensional cubes are presented. We also prove the converse of the Dranishnikov-Uspenskij theorem on dimension-raising maps.
引用
@article{arxiv.math/0301004,
title = {Extraordinary dimension theories generated by complexes},
author = {A. Chigogidze},
journal= {arXiv preprint arXiv:math/0301004},
year = {2007}
}