In commutative algebra, the constructible topology on the spectrum of a commutative ring is a topology where each closed set is the image of in for some algebra B over A. An important feature of this construction is that the map is a closed map with respect to the constructible topology.
With respect to this topology, is a compact, Hausdorff, and totally disconnected topological space. In general the constructible topology is a finer topology than the Zariski topology, but the two topologies will coincide if and only if is a von Neumann regular ring, where is the nilradical of A.
Despite the terminology being similar, the constructible topology is not the same as the set of all constructible sets.
- Some authors prefer the term quasicompact here.
- "Reconciling two different definitions of constructible sets". math.stackexchange.com. Retrieved 2016-10-13.
- Atiyah, Michael Francis; Macdonald, I.G. (1969), Introduction to Commutative Algebra, Westview Press, p. 87, ISBN 978-0-201-40751-8
- Knight, J. T. (1971), Commutative Algebra, Cambridge University Press, pp. 121–123, ISBN 0-521-08193-9