Proximity inductive dimension and Brouwer dimension agree on compact Hausdorff spaces
General Topology
2021-08-17 v1
Abstract
In this paper we show that the proximity inductive dimension defined by Isbell agrees with the Brouwer dimension originally described by Brouwer on the class of compact Hausdorff spaces. Consequently, Fedorchuk's example of a compact Hausdorff space whose Brouwer dimension exceeds its Lebesgue covering dimension is an example of a space whose proximity inductive dimension exceeds its proximity dimension as defined by Smirnov.
Keywords
Cite
@article{arxiv.1903.01586,
title = {Proximity inductive dimension and Brouwer dimension agree on compact Hausdorff spaces},
author = {Jeremy Siegert},
journal= {arXiv preprint arXiv:1903.01586},
year = {2021}
}
Comments
8 pages