Conjectures and Counterexamples

Lynn Arthur Steen and J. Arthur Seebach
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Lynn Arthur Steen: Saint Olaf College
J. Arthur Seebach: Saint Olaf College

A chapter in Counterexamples in Topology, 1978, pp 161-181 from Springer

Abstract: Abstract The search for necessary and sufficient conditions for the metrizability of topological spaces in one of the oldest and most productive problems of point set topology. Alexandroff and Urysohn [6] provided one solution as early as 1923 by imposing special conditions on a sequence of open conversing. Nearly ten years later R.L. Moore chose to begin his classic text on the Foundations of Point Set Theory [82] with an axiom structure which was a slight variation of the Alexandroff and Urysohn metrizability conditions. After Jones [56], we now call any space which satisfies Axion 0 and parts 1, 2, 3 of Axiom 1 of [82] a Moore space. Each metric space is a Moore space, but not conversely, so the search for a metrization theorem became that of determining precisely which Moore spaces are metrizable. The most famous conjecture was that each normal Moore space is metrizable.

Keywords: Continuum Hypothesis; Regular Space; Paracompact Space; Uniform Base; Metrization Theory (search for similar items in EconPapers)
Date: 1978
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DOI: 10.1007/978-1-4612-6290-9_7

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