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- W4313256523 abstract "It is an interesting, maybe surprising, fact that different dense subspaces of even “nice” topological spaces can have different densities. So, our aim here is to investigate the set of densities of all dense subspaces of a topological space X that we call the double density spectrum of X and denote by dd(X). We improve a result from [1] by showing that dd(X) is always ω-closed (i.e., countably closed) if X is Hausdorff. We manage to give complete characterizations of the double density spectra of Hausdorff and of regular spaces as follows. Let S be a non-empty set of infinite cardinals. Then We also prove a number of consistency results concerning the double density spectra of compact spaces. For instance:" @default.
- W4313256523 created "2023-01-06" @default.
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- W4313256523 date "2022-12-27" @default.
- W4313256523 modified "2023-10-14" @default.
- W4313256523 title "The double density spectrum of a topological space" @default.
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- W4313256523 doi "https://doi.org/10.1007/s11856-022-2453-9" @default.
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