On The Generalized Topological Set Extension Results Using The Cluster Point Approach On The Generalized Topological Set Extension Results Using The Cluster Point Approach

Abstract

In this work, we seek generalized finite extensions for a set of real numbers in the topological space through the cluster point approach. Basically, we know that in the topological space, a point is said to be a cluster point of a subset X if and only if every open set containing the point say x contains another point of x1 different from x. This concept with the aid basic known ideas on set theory was carefully used in the definition of linear, radial, and circular types of operators which played the major roles in realizing generalized extension results as in our main results of section three.