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- W1987222044 abstract "All spaces are assumed to be regular Hausdorff topological spaces. If X and Y are spaces, then an open set U in X×Y is an open universal set parametrized by Y if for each open set V of X, there is y∈Y such that V={x∈X:(x,y)∈U}. A space Y is said to parametrize W(κ) if Y parametrizes an open universal set of each space of weight less than or equal to κ. The following are the important results of this paper. If a metrizable space of weight κ parametrizes W(κ), then κ has countable cofinality. If κ is a strong limit of countable cofinality, then there is a metrizable space of weight κ parametrizing W(κ). It is consistent and independent that there is a cardinal κ of countable cofinality, but not a strong limit, and a metrizable space of weight κ parametrizing W(κ). It is consistent and independent that a zero-dimensional, compact first countable space parametrizing itself (equivalently, parametrizing all spaces of the same or smaller weight) must be metrizable." @default.
- W1987222044 created "2016-06-24" @default.
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- W1987222044 date "2002-04-01" @default.
- W1987222044 modified "2023-09-27" @default.
- W1987222044 title "Parametrizing open universals" @default.
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- W1987222044 doi "https://doi.org/10.1016/s0166-8641(01)00069-4" @default.
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