Continuous images of linearly ordered continua and compacta

The Mardešić Conjecture and free products of Boolean algebras

“…, 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].…”

“…where 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].…”

“…On the other hand, Avilés [1] proved that, under the assumptions of 1.1, there are at least s + 1 separable factors K j . This result, combined with Mardešić's result mentioned above, implies that if a product of two linearly ordered compact spaces can be mapped onto a product of three infinite compact spaces K 1 , K 2 , K 3 , then at least one K j is metrizable [1,8].…”

“…K d+s with s ≥ 1, then there are at least s + 1 metrizable factors K j . In the same paper he raised a question, if the separability assumption may be dropped, stating the following conjecture (see also the survey paper [8]): Conjecture 1.1. If a product of d linearly ordered compact spaces can be mapped onto a product of d + s infinite compact spaces K 1 , K 2 , .…”

“…K d+s with s ≥ 1, then there are at least s + 1 metrizable factors K j . In the same paper he raised a question, if the separability assumption may be dropped, stating the following conjecture (see also the survey paper [8]):…”