Let \(R\) be an associative ring with an identity element. \(R\)-space is the collection of isomorphism classes of simple \(R\)-modules. For each \(p\) from \(R\)-space denote by \(N_p\) a chosen representative of \(p\). A subset \(X\) of \(R\)-space is algebraic if the isomorphism class of each simple subquotient of \(\prod_{p\in X}N_p\) is contained in \(X\). It is shown that \(R\)-space is a topological space with algebraic sets being closed. This topology is a refinement of the Jacobson topology which is defined in the following way. If \(I\triangleleft R\) is a two-sided ideal then \(v(I)\) is the collection of all \(p\) from \(R\)-space such that \(Ip=0\). The Jacobson topology is the topology in which \(v(I)\) are closed. Suppose that there exists a Noetherian module \(E\) which maps onto each simple \(R\)-module. Then \(R\)-space is a Noetherian topological space. The coincidence of \(R\)-topology and Jacobson topologies and a comparison with Rosenberg’s spectra is discussed. All considerations are made in the more general setting of any complete Abelian category.