  When finding an original proof to a known result describing expansive
mappings 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.
