Abstract

Let X be a perfect separable complete metric space. Let G = (V; E) be a simple graph such that V ` X . Let ~ E = f(x; y) j fx; yg 2 Eg. We call G analytic if ~ E is an analytic subset of X 2 . Similarly, G is oe-analytic if ~ E belongs to the oe-algebra generated by all the analytic subsets of X 2 . We call G a weighted graph if an ordinal is assigned to every edge. Let G be an analytic connected weighted graph. We prove that under some restrictions G has a oe-analytic minimal spanning tree T (i.e, if we replace one edge in T by a lighter edge, then T stops being a spanning tree). We also give examples that show that this result is optimal.

Citations