Poorly separated infinite normal products
General Topology
2020-02-10 v1
Abstract
A product of compact normal spaces is normal; the product of a countably infinite collection of non-trivial spaces is normal if and only if it is countably paracompact and each of its finite sub-products is normal; if all powers of a space X are normal then X is compact: provided in each case that the spaces involved are T1. Here I examine the situation for infinite products not required to be T1 (or regular), extending or generalizing each of these facts. In addition, I prove some related results, give a number of examples, explore some alternative proofs, and close with some speculation regarding potential applications of these findings to category theory and lattice theory.
Keywords
Cite
@article{arxiv.2002.02483,
title = {Poorly separated infinite normal products},
author = {N. Noble},
journal= {arXiv preprint arXiv:2002.02483},
year = {2020}
}
Comments
38 pages