Uniqueness Conditions of the Representation of a Topology in \[{ Top}(X)\]

In this article motivated by unique representation of a topology \[\tau \] on X, we introduce some kind of representation for \[\tau \] in \[{ Top}(X)\] and find the equivalent condition for a topological space to have unique representation. As the main part of the paper, we introduce the natural representation for every topology \[\tau \] on a set X of the form \[\bigwedge _{a\in L(X)}\mathscr {T}(a,\mathscr {W}_a)\], where \[\mathscr {W}_a\] is the set of all neighborhoods and deleted neighborhoods of a and L(X) is the set of all non-isolated points of X, and we characterize the spaces whose topology has unique representation. Also it is proved that every first countable Hausdorff space has unique representation property.