Search results for "54F65"

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Urysohn's metrization theorem for higher cardinals

2011

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.

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

2015

We establish equivalences between compacta that admit a sequence of retractions that converge uniformly to the identity map and compacta that are inverse limits on subcompacta with retractions for bonding maps. We give partial answers to questions of Charatonik and Prajs, and of Krasinkiewicz. Our results are related to and use results from another paper of the authors \cite{mp}.

Discrete mathematicsSequenceGeneral Mathematics54A20Inverse$r$-maps54F6554C15retractions54F15CalculusIdentity functionInternal inverse limitMathematics
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