If X is a completely regular space, first we characterize those spaces C-b(X) whose compact sets are metrizable. Then we use this result to provide a general condition for X to ensure themetrizability of compact sets in C-b(X). Finally, we characterize those spaces C-b(X) that have a G-basis.
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Univ Autonoma Metropolitana, Dept Math, Av San Rafael Atlixco 186, Mexico City 09340, DF, MexicoUniv Autonoma Metropolitana, Dept Math, Av San Rafael Atlixco 186, Mexico City 09340, DF, Mexico
Hernandez, Constancio
Tkachenko, Mikhail
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Univ Autonoma Metropolitana, Dept Math, Av San Rafael Atlixco 186, Mexico City 09340, DF, MexicoUniv Autonoma Metropolitana, Dept Math, Av San Rafael Atlixco 186, Mexico City 09340, DF, Mexico