Spezialisierungen im reellen Spektrum zu einer komplexen Varietät. (Specializations in real spectrum to a complex variety.) (Q1814107)

By restriction of scalars, every affine complex variety \(X\) defines an affine real variety \(r_{\mathbb{C}\mid \mathbb{R}}(X)\). This paper studies the specializations of the real spectrum associated with \(r_{\mathbb{C}\mid \mathbb{R}}(X)\). As an application we prove that, for a morphism \(f:X\to Y\) of complex varieties, the set of points of \(X\) at which \(f\) is universally open is constructible in \(X\) and \(f\) is universally open at a point \(x\in X(\mathbb{C})\) if and only if \(f_ \mathbb{C}:X(\mathbb{C})\to Y(\mathbb{C})\) is open at \(x\) in the strong topologies of \(X(\mathbb{C})\) and \(Y(\mathbb{C})\).