= Continuous array in better-quasi-order theory
{title2=$F:[A]^\omega\to Q$}
= Continuous arrays in better-quasi-order theory
{synonym}
A continuous array takes infinite subsets of an infinite $A\subseteq\omega$, in the <ordinary topology on infinite subsets>, to a discrete <preorder> $Q$. It is bad if $F(X)\not\leq F(X\setminus\{\min X\})$ for every infinite $X$. A <barrier in better-quasi-order theory> array induces such a continuous array by evaluating its unique barrier initial segment. The continuous-array and barrier formulations of <better-quasi-ordering> are equivalent, using refinement of fronts to barriers in the reverse direction.
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