Generalization of Two Wolk' s Theorems

Abstract:

      In his paper [1] E.S. Wolk generalized Dini theorem and another classical theorem. In Wolk's theorems ranges are partially ordered sets with Dedekind topology in which totally unordered subsets are finite. In this paper by Wolk's problem interval topology in partially ordered sets is substituted for Dedekind topology without the finiteness condition on totally unordered subsets of ranges, and Wolk's theorems become the direct corollaries of our results.