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Generalization of Scott's formula for retractions from generalized Alexandroff's cube by Jarosław Achinger is a Computer Science article available to read on EtoBox.

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In the paper [2] the following theorem isshowu: Theorem (Th. 3,5, [2]), Ira = 0 or 6 = oo or a> 6, then a closure space X is an absolute extensor for the category of -closure spaces iff a contraction of X is the closure space of all -filters in an -semidistribntive lattice. In the case when a = ~o and 6 = oo, this theorem becomes Scott's theorem: Theorem ([7]). A topologieM space X is an absolute extensor for the category of all topological spaces iff a contraction of X is a topological space of "Scott's open sets" in a continuous lattice. On the other hand, when a = 0 and 6 = o), this theorem becomes Jankowski's theorem : Theorem ([4]). A closure space X is an absolute extensor for the category of all closure spaces satisfying the compactness theorem iff a contraction of X is a closure space of all filters in a complete Keyting lattice. But for separate cases of a and 6, the Theorem 3.5 from [2] is proved using essen. tialy different methods. In this paper it is shown that this theorem can be proved using, for retraction, one uniform formula. hramely it is proved that if a = 0 or 6 = ~ or a > 6 and F~,~ (L) c B ~ and if 15 is an -semidistributive lattice, then the function r:

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Author

Jarosław Achinger

Publisher

Springer Netherlands; Springer-Verlag; Kluwer Academic Publishers; Springer Science and Business Media LLC (ISSN 0039-3215)

Published

1986

Language

EN

Field

Computer Science (Physical Sciences)