 The set of pairs that constitute a (unary) function is sometimes called the graph of the function. The graph of a continuous function \(f\colon P\omega\rightarrow P\omega\) is defined by \(\textrm{graph}(f)=\{(n,m)\colon  m\in f(e_n)\}\). In order to be able to model type-free application—including self-application—subsets of \(\omega\) should be viewed as functions too. For \(x, y\subseteq\omega\), the function determined by \(y\) is defined as \(\textrm{fun}(y)(x)=\{m\colon \exists e_n\subseteq x.\,(n,m)\in y\}\). For a continuous function \(f\),  \(\textrm{fun}(\textrm{graph}(f))=f\) holds.