(Quasi)-uniformities on the set of bounded maps

Abstract

From real analysis it is known that if a sequence {fn,   n∈ℕ} of real-valued functions defined and bounded on X⊂ℝ converges uniformly to f, then f is also bounded and the sequence {fn,   n∈ℕ}. In the present paper we generalize results as the above using (quasi)-uniform structures.