nLab
irreducible topological space

A topological space XX is irreducible if it can not be expressed as union of two proper closed subsets, or equivalently if any two inhabited open subsets have inhabited intersection. A subset SS of a topological space XX is an irreducible subset if SS is an irreducible topological space with the induced topology. An algebraic variety is irreducible if its underlying topological space (in the Zariski topology) is irreducible.

Contrast this with a sober space, where the only irreducible closed subsets are the points.

Revised on April 9, 2015 16:41:49 by A. Gagna? (82.170.147.99)