Ample continua in Cartesian products of continua

TL;DR

This paper proves that certain products of continua, including arcs, solenoids, and pseudo-arcs, possess the fupcon property, answering open questions in continuum theory.

Contribution

It establishes the fupcon property for products of specific continua, extending previous results and resolving open questions in the field.

Findings

Product of arc and solenoid has fupcon property

Product of Knaster continuum and solenoid has fupcon property

Product of two Smith's pseudo-arcs has fupcon property

Abstract

We show that the Cartesian product of the arc and a solenoid has the fupcon property, therefore answering a question raised by Illanes. This combined with Illanes' result implies that the product of a Knaster continuum and a solenoid has the fupcon property, therefore answering a question raised by Bellamy and \L ysko in the affirmative. Finally, we show that a product of two Smith's nonmetric pseudo-arcs has the fupcon property.