The essential cover and the absolute cover of a schematic space

• Autorzy: Wolfgang Rump , Yi Chuan Yang
• Języki publikacji: EN

Abstrakty

EN

A theorem of Gleason states that every compact space admits a projective cover. More generally, in the category of topological spaces with continuous maps, covers exist with respect to the full subcategory of extremally disconnected spaces. Such a cover of a space is called its absolute. We prove that the absolute exists within the category of schematic spaces, i.e. the spaces underlying a scheme. For a schematic space, we use the absolute to generalize Bourbaki's concept of irreducible component, so that embedded and multiple components may arise. We introduce the essential cover of a schematic space, and show that it parametrizes the generalized components.

Kategorie tematyczne

• 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces
• 06D05: Structure and representation theory
• 54G05: Extremally disconnected spaces, F -spaces, etc.
• 54A05: Topological spaces and generalizations (closure spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 114
• Numer: 1
• Strony: 53-75

Daty

wydano

2009

Twórcy

autor

Wolfgang Rump

• Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany

autor

Yi Chuan Yang

• Department of Mathematics & LMIB, Beihang University, Beijing 100083, P.R. China

Identyfikatory

DOI

10.4064/cm114-1-6