Poorly separated infinite normal products

N. Noble

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arXiv · 2002.02483

Poorly separated infinite normal products

N. Noble

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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.

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N. Noble. 2020-02-06. Poorly separated infinite normal products. https://arxiv.org/abs/2002.02483

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