(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.

Keywords

• function spaces
• uniformity of uniform convergence
• set of bounded functions.