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Urysohn's metrization theorem for higher cardinals

Joonas Ilmavirta

subject

Mathematics::Logic54F65 54C25 54A25 54D70 54D10 54D20General Topology (math.GN)FOS: MathematicsMathematics::General TopologyAstrophysics::Cosmology and Extragalactic AstrophysicsMathematics - General Topology

description

In this paper a generalization of Urysohn's metrization theorem is given for higher cardinals. Namely, it is shown that a topological space with a basis of cardinality at most $|\omega_\mu|$ or smaller is $\omega_\mu$-metrizable if and only if it is $\omega_\mu$-additive and regular, or, equivalently, $\omega_\mu$-additive, zero-dimensional, and T\textsubscript{0}. Furthermore, all such spaces are shown to be embeddable in a suitable generalization of Hilbert's cube.

yearjournalcountryeditionlanguage
2011-05-23
https://dx.doi.org/10.48550/arxiv.1105.4463