Hereditarily indecomposable continua as generic objects

Adam Bartoš, Wiesław Kubiś

Published 2022-08-14Version 1

We develop an abstract approximate Fra\"iss\'e theory in order to realize the pseudo-arc as well as P-adic pseudo-solenoids for sets of primes P as Fra\"iss\'e limits. Our framework generalizes the discrete theory (classical and projective), but is also suitable for working directly with continuous maps on metrizable compacta. Moreover, we consider the abstract Banach--Mazur game played in a category and realize the pseudo-arc as well as all pseudo-solenoids (not necessarily P-adic) as generic objects.