On expansions
arXiv:1908.04916
Abstract
When finding an original proof to a known result describing expansions on compact metric spaces as surjective isometries, we reveal that relaxing the condition of compactness to total boundedness preserves the isometry property and nearly that of surjectivity. While a counterexample is found showing that the converse to the above descriptions do not hold, we are able to characterize boundedness in terms of specific expansions we call anticontractions.
Various modifications, including the title, updated bibliography