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


  1. Some authors prefer the term quasicompact here.
  2. "Reconciling two different definitions of constructible sets". Retrieved 2016-10-13.

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