Mardešić conjecture and free products of Boolean algebras

Gonzalo Martínez-Cervantes; Grzegorz Plebanek

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arXiv · 1711.10395

Mardešić conjecture and free products of Boolean algebras

Gonzalo Martínez-Cervantes·Grzegorz Plebanek

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Abstract

We show that for every $d\ge 1$, if $L_1,\ldots, L_d$ are linearly ordered compact spaces and there is a continuous surjection \[ L_1\times L_2\times \dots\times L_d\to K_1\times K_2\times\ldots\times K_{d}\times K_{d+1},\] where all the spaces $K_i$ are infinite, then $K_i, K_j$ are metrizable for some $1\le i<j\le d+1$. 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.

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BibTeX RIS

Gonzalo Martínez-Cervantes, Grzegorz Plebanek. 2017-11-28. Mardešić conjecture and free products of Boolean algebras. https://arxiv.org/abs/1711.10395

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