Properties of Nonmetric Hereditarily Indecomposable Subcontinua of Finite Products of Lexicographic Arcs

Abstract

Nonmetric hereditarily indecomposable subcontinua of finite products of Lexicographic arcs are examined. It is shown that these subcontinua cannot intersect certain subsets of the products. Then nonmetric hereditarily indecomposable subcontinua of these same products cross the Hilbert cubes are examined and are shown to not intersect certain subsets. In conclusion, it is shown that all hereditarily indecomposable subcontinua of the product of three Lexicographic arcs are metric.