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

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.