A Few Properties of $\delta$-Continuity and $\delta$-Closure on Delta Weak Topological Spaces

TL;DR

This paper investigates properties of $\,delta$-continuity and $\,delta$-closure in delta weak topological spaces, defining a minimal topology that preserves $\,delta$-continuity of functionals and exploring their relations and closures.

Contribution

It introduces a weakest topology ensuring $\,delta$-continuity of functionals and analyzes the relationship between $\,delta$-continuous functionals and $\,delta$-closure in delta weak topological spaces.

Findings

Defined the weakest topology preserving $\,delta$-continuity.

Established the relation between $\,delta$-continuous functionals on original and weakest topology.

Characterized the $\,delta$-closure of subsets in the new topology.

Abstract

The main aim of this paper is to define a weakest topology $\sigma$ on a linear topological space $(E, \tau)$ such that each $\delta$-continuous functional on $(E, \tau)$ is $\delta$-continuous functional on $(E, \sigma)$ and to find out the relation between the set of these $\delta$-continuous functionals on $(E, \tau)$ and the set of all $\delta$-continuous functionals on $(E, \sigma)$. Also we find out the closure of a subset $A$ of $E$ on that weakest topology by the $\delta$-closure of $A$ with respect to the given topology.