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From well to better, the space of ideals

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Carroy R., Pequignot Y.

Fundamenta Mathematicae

2014

tom 227

nr 3

247-270

On the one hand, the ideals of a well quasi-order (wqo) naturally form a compact topological space into which the wqo embeds. On the other hand, Nash-Williams' barriers are given a uniform structure by embedding them into the Cantor space. We prove that every map from a barrier into a wqo restricts on a barrier to a uniformly continuous map, and therefore extends to a continuous map from a countable closed subset of the Cantor space into the space of ideals of the wqo. We then prove that, by shrinking further, any such continuous map admits a canonical form with regard to the points whose image is not isolated. cr As a consequence, we obtain a simple proof of a result on better quasi-orders (bqo); namely, a wqo whose set of non-principal ideals is a bqo is actually a bqo.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Carroy R.

1 Pequignot Y.

1 2014

Wyniki wyszukiwania

From well to better, the space of ideals