ABSTRACT
We prove a Hausdorff ring topology on a field is locally bounded if and only if it is induced by a function which we call a near valuation. Near valuations are easier to construct and to work with than the set valued generalized valuations Nakano used to induce the class of locally bounded topologies. In connection with near valuations, it is natural to use a definition of valuation due to Kowalsky and Diirbaum, which is somewhat more general than the usual one. Standard theorems of valuation theory are considered from this slightly more general point of view.
