2020/02/06 by N. Noble, Noble, N.
Mathematics · #06B35 #18B30 #54C15 #54C30 #54D10 #54D15 #54D20 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Primary 54B10 #Rings, Modules, and Algebras #secondary 54C10
paper · pdf · doi:10.48550/arxiv.2002.02483
openalex publication_date 2020/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.