Kolloquien und Oberseminare Übersicht Detail

Vortragende Person/Vortragende Personen:
Herr Prof. Dr. Niels Schwartz (Universität Passau)

Diese Veranstaltung ist Teil der Veranstaltungsreihe „Schwerpunktskolloquium Reelle Geometrie und Algebra“.

Abstract: The spectral spaces (with the spectral maps as morphisms) form a subcategory, Spec, of the category Top of topological spaces. Spectral spaces can be defined by a list of topological properties. As Hochster showed, they are the Zariski spectra of rings (commutative with unit), equivalently the prime ideal spectra of bounded distributive lattices (Stone). The lecture focuses on the relationship between Spec and Top. It is a rather simple fact that Spec is a reflective subcategory of Top. The spectral reflection of a topological space belongs to a special class of spectral spaces, which are called localic spaces. These also arise naturally in the area of pointfree topology. The relationship between a topological space and its spectral reflection will be explained.