# Constructible topology

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,^{[1]} 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.^{[2]}

## See also

## References

- ↑ 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

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