Let (X,d) be an unbounded metric space. A sequence in X is called convergent to infinity in distance provided is eventually outside any bounded subset. By a metric mode of convergence to infinity in a regular Hausdorff space X, we mean a sequence of closed subsets of X with and. In a regular Haudorff space, we call a nonnegative continuous function $f$ a forcing function for a metric mode of convergence to infinity rovided if and only if. A sequence (or net) in X is convergent to infinity with respect to rovided for each k, contains eventually. Modulo a natural equivalence relation, these correspond to one-point extensions of the space with a countable base at the ideal point, and in the metrizable setting, they correspond to metric boundedness structures for the space. In this thesis, we study the interplay between these objects and certain continuous functions that may determine the proof that each noncompact metrizable space admits uncountably much distinct metric uniformity.