Ultraparacompactness and Ultranormality

2013/06/25 by Joseph Van Name, Van Name, Joseph · 2 voices
Mathematics · #54D15 #54D20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras #math.GN #msc:54D15 #msc:54D20

paper · pdf · doi:10.48550/arxiv.1306.6086

These are simply notes on ultranormality and ultraparacompactness. These notes are currently not intended to be published in a journal

arxiv created 2013/06/25 · openalex publication_date 2013/06/25 · arxiv published 2013/06/25 · arxiv updated 2013/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we shall overview some results related to ultraparacompactness and ultranormality in the general topological and point-free contexts. This note contains some standard results and counterexamples along with some results which are not that well known and even of my new results.

Discussions

• Question: Does the topos $\mathbf{Sh}(\mathcal{B})$ of sheaves on Baire space $\mathcal{B} := \mathbb{N}^{\mathbb{N}}$ (with the usual product topology) satisfy the following Choice principle (★) belo [stackexchange, 5 points]
• … Maybe this is because “ultranormal” is equivalent to “normal and strongly zero-dimensional” (but “strongly zero-dimensional”, despite being more standard, is less obvious to define). Anyway, this no [bsky, 2 points, 1 comments]

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