Covering dimension and finite-to-one maps
General Topology
2014-01-15 v1 Logic
Abstract
Hurewicz' characterized the dimension of separable metrizable spaces by means of finite-to-one maps. We investigate whether this characterization also holds in the class of compact F-spaces of weight c. Our main result is that, assuming the Continuum Hypothesis, an n-dimensional compact F-space of weight c is the continuous image of a zero-dimensional compact Hausdorff space by an at most 2n-to-1 map.
Cite
@article{arxiv.0910.4107,
title = {Covering dimension and finite-to-one maps},
author = {Klaas Pieter Hart and Jan van Mill},
journal= {arXiv preprint arXiv:0910.4107},
year = {2014}
}