“Scattered order”的意思、由来-开放百科全书

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Scattered order

释义

References

{{otheruses4|order theory|the Australian post-punk band|Scattered Order}}

In mathematical order theory, a scattered order is a linear order that contains no densely ordered subset with more than one element (Harzheim 2005:193ff.)

A characterization due to Hausdorff states that the class of all scattered orders is the smallest class of linear orders which contains the singleton orders and is closed under well-ordered and reverse well-ordered sums.

Laver's theorem (generalizing Fraïssé's conjecture) states that the embedding relation on the class of countable unions of scattered orders is a well-quasi-order (Harzheim 2005:265).

The order topology of a scattered order is scattered. The converse implication does not hold, as witnessed by the lexicographic order on .

References

{{cite book|author=Egbert Harzheim

|title=Ordered Sets|year=2005|publisher=Springer|isbn=0-387-24219-8}}

{{cite journal|first=Richard|last=Laver|title=On Fraïssé's order type conjecture|journal=Annals of Mathematics|volume=93|year=1971|number=1|pages=89–111|jstor=1970754 | doi = 10.2307/1970754}}

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