Relative Almost Uniform Convergent Sequence of Functions and Its Topological Properties

Kshetrimayum Renubebeta Devi; Pranab Jyoti Dowari; Yangambam Nongpoknganba  Meitei

doi:10.5269/bspm.77965

Relative Almost Uniform Convergent Sequence of Functions and Its Topological Properties

Authors

Kshetrimayum Renubebeta Devi The Assam Royal Global University, Guwahati https://orcid.org/0000-0003-2819-3193
Pranab Jyoti Dowari Department of Mathematics, Moridhal College, Dhemaji-787057, Assam, India https://orcid.org/0000-0002-7834-9021
Yangambam Nongpoknganba Meitei Department of Mathematics, Kha Manipur College Kakching, Manipur, India https://orcid.org/0009-0009-4191-3547

DOI:

https://doi.org/10.5269/bspm.77965

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.