Mardešić conjecture and free products of Boolean algebras

الأصل · EN

We show that for every d≥ 1, if L₁,, Ld are linearly ordered compact spaces and there is a continuous surjection L₁× L₂× × Ld→ K₁× K₂×× Kd× Kd₊₁, where all the spaces Kᵢ are infinite, then Kᵢ, Kⱼ are metrizable for some 1≤ i<j≤ d+1. This answers a problem posed by S. Mardešić. 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 by L. Baur and L. Heindorf.