Single set in a topology What is meant by a single set in a topological space? The statement goes as: "let $X$ and $X'$ denote a single set in the topologies $\mathcal{T}$ and $\mathcal{T'}$ respectively".

Here means,for example,a $\mathbf{one}$ set,say, $X_{0}$ endowed with two different topologies $\mathcal{T}$ and $\mathcal{T}'$, because in views of their different topologies,a $\mathbf{single}$ set $X_{0}$ could be two different topological spaces, namely $X$ and $X'$ respectively.But as sets,$X=X'$.
