A study of uniformities on the space of uniformly continuous mappings

Abstract

New families of uniformities are introduced on UC(X,Y)UC(X,Y), the class of uniformly continuous mappings between X and Y, where (X,U)(X,{\mathcal{U}}) and (Y,V)(Y,{\mathcal{V}}) are uniform spaces. Admissibility and splittingness are introduced and investigated for such uniformities. Net theory is developed to provide characterizations of admissibility and splittingness of these spaces. It is shown that the point-entourage uniform space is splitting while the entourage-entourage uniform space is admissible.

Keywords

• uniform space
• function space
• splittingness
• admissibility
• uniformly continuous mappings
• 54c35
• 54a20