Urysohn's metrization theorem for higher cardinals

Details Urysohn's metrization theorem for higher cardinals Urysohn's metrization theorem for higher cardinals

2011-05-23

arxiv.org/abs/1105.4463v1

Mathematics

General Topology

8 pages, no figures

Scientific paper

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.

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