Let \(M\) be a set and \(C\) be a nonempty set of real or complex functions on \(M\). \(M\) carries the smallest topology in which all functions from \(C\) are continuous. A pair \((M, C)\) is called a \(d^ r\)-space over \(\mathbf K\) (\({\mathbf K} = \mathbb{R}\) or \({\mathbf K} = \mathbb{C}\), \(r \in \mathbb{N}_ 0 \cup \{\infty, \omega\}\)) if for any \(f_ 1, \dots, f_ n \in C\) and \(\sigma \in C^ r\) (\({\mathbf K}^ n, {\mathbf K})\) the composition \(\sigma \circ (f_ 1, \dots, f_ n) \in C\) and \(C = C_ M\), where \(C_ M\) is the set of functions \(M \to {\mathbf K}\) locally belonging to \(C\). The author presents some interesting examples of \(d^ r\)-spaces in electrical engineering. In Section 3 definitions of a \(d^ s\)-tensor field and a \(C^ s\)-tensor field on a \(d^ r\)-space \((M, C)\) are given. The concept of an exterior derivative is presented (Theorem 1).