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- W2549838218 abstract "Denote by $mathbf C_p[mathfrak M_0]$ the $C_p$-stable closure of the class $mathfrak M_0$ of all separable metrizable spaces, i.e., $mathbf C_p[mathfrak M_0]$ is the smallest class of topological spaces that contains $mathfrak M_0$ and is closed under taking subspaces, homeomorphic images, countable topological sums, countable Tychonoff products, and function spaces $C_p(X,Y)$. Using a recent deep result of Chernikov and Shelah (2014), we prove that $mathbf C_p[mathfrak M_0]$ coincides with the class of all Tychonoff spaces of cardinality strictly less than $beth_{omega_1}$. Being motivated by the theory of Generalized Metric Spaces, we characterize also other natural $C_p$-type stable closures of the class $mathfrak M_0$." @default.
- W2549838218 created "2016-11-30" @default.
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- W2549838218 date "2017-01-01" @default.
- W2549838218 modified "2023-09-24" @default.
- W2549838218 title "The $C_p$-stable closure of the class of separable metrizable spaces" @default.
- W2549838218 doi "https://doi.org/10.4064/cm6475-3-2016" @default.
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