From well to better, the space of ideals

Raphaël Carroy, and Yann Pequignot. "From well to better, the space of ideals." Fundamenta Mathematicae 227.3 (2014): 247-270. <http://eudml.org/doc/283258>.

@article{RaphaëlCarroy2014,
abstract = { 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. },
author = {Raphaël Carroy, Yann Pequignot},
journal = {Fundamenta Mathematicae},
keywords = {well quasi-order; better quasi-order; ideal; uniform continuity; barrier},
language = {eng},
number = {3},
pages = {247-270},
title = {From well to better, the space of ideals},
url = {http://eudml.org/doc/283258},
volume = {227},
year = {2014},
}

TY - JOUR
AU - Raphaël Carroy
AU - Yann Pequignot
TI - From well to better, the space of ideals
JO - Fundamenta Mathematicae
PY - 2014
VL - 227
IS - 3
SP - 247
EP - 270
AB - 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.
LA - eng
KW - well quasi-order; better quasi-order; ideal; uniform continuity; barrier
UR - http://eudml.org/doc/283258
ER -