The Abbott dimension of Hausdorff spaces

Abbott Dimension, Mathematics Inspired by Flatland

We introduce the abbott dimension of hausdorff spaces, an intuitively defined dimension function inspired by edwin abbott s\emph{flatland}.We show that on separable metric spaces the abbott dimension is bounded above by the large inductive dimension.We conclude by showing thathereditarily indecomposable continua all have abbott dimension while thereexist such continua of arbitrarily high large inductive, small inductive, and coveringing dimension.