Relative Almost Uniform Convergent Sequence of Functions and Its Topological Properties

Abstract

This paper introduces the concept of almost convergence for sequences of functions with respect to a scale function. We examine foundational properties such as linearity and completeness, and define the classes of relatively almost convergent, relatively null, and relatively bounded sequences of functions. In addition, we explore various topological aspects of the space including convexity, strict convexity, separability, and symmetry.