Cascades and multifilters (Q1568399)
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scientific article; zbMATH DE number 1462693
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Cascades and multifilters |
scientific article; zbMATH DE number 1462693 |
Statements
Cascades and multifilters (English)
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23 January 2001
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A cascade is a tree (with smallest element) having finite branches only and such that every non-maximal element is a filter on the set of immediate successors. A multifilter in \(X\) is a mapping into \(X\) defined on a cascade (not on the least element). After proving some facts about cascades, multifilters and other related concepts, it is shown that a point \(x\) belongs to a closure (determined by a convergence) of a set \(A\) iff there exists a multifilter starting from \(A\) and converging to \(a\).
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convergence
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multisequence
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multifilter
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