Concepedia

Paracompactness of Metric Spaces and the Axiom of Multiple Choice

Paul C. Howard, Kyriakos Keremedis, Jean E. Rubin, Adrienne Stanley

Mathematical logic quarterly · 2000 · 12 citations · 8 references

DOI

Concepts

Abstract

The axiom of multiple choice implies that metric spaces are paracompact but the reverse implication cannot be proved in set theory without the axiom of choice.

References

8

Metrization of Topological Spaces

R. H. Bing · Canadian Journal of Mathematics · 1951 · 478 citations · Full text

, , +13

Distance functions and the metrization problem

Alexander Frink · Bulletin of the American Mathematical Society · 1937 · 208 citations · Full text

, , +11

Remark on the concept of compactness

Richard Arens, J. Dugundji · Portugaliae Mathematica · 1950 · 62 citations

, , +4

A new proof that metric spaces are paracompact

Mary Ellen Rudin · Proceedings of the American Mathematical Society · 1969 · 58 citations · Full text

, , +7

Axioms of multiple choice

Amit Levy · Fundamenta Mathematicae · 1962 · 57 citations · Full text

, , +7