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- W2079741947 abstract "The collection of test spaces for the ordinal invariant σ on the category of regular sequential topological spaces is determined. The spaces K α , α < w 1 defined by Archangel'skiǐ and Franklin are shown to have this property. To establish this a collection of spaces T and a topological extension for the spaces in T 1 the principal extension, are defined. In particular, if X is a regular sequential space and σ ( X )= α < ω 1 , then X contains a subspace T α ϵ T such that the principal extension of T α is K α . Furthermore, if X is a Hausdorff sequential space which contains a copy of K α , then σ ( X )⩾ α . A variety of sequential closure formulas are derived and several examples are presented." @default.
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- W2079741947 date "1982-01-01" @default.
- W2079741947 modified "2023-09-27" @default.
- W2079741947 title "Test spaces for infinite sequential order" @default.
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- W2079741947 doi "https://doi.org/10.1016/0166-8641(82)90052-9" @default.
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