The Mardešić Conjecture and free products of Boolean algebras

Abstract

We show that for every d ≥ 1, if L 1 , . . . , L d are linearly ordered compact spaces and there is a continuous surjectionwhere all the spaces K i are infinite, then K i , K j are metrizable for some 1 ≤ i < j ≤ d + 1. This answers a problem posed by Mardešić [7,8].We present some related results on Boolean algebras not containing free products with too many uncountable factors. In particular, we answer a problem on initial chain algebras that was posed in [3].