On definably proper maps

• Autorzy: Mário J. Edmundo , Marcello Mamino , Luca Prelli
• Języki publikacji: EN

Abstrakty

EN

In this paper we work in o-minimal structures with definable Skolem functions, and show that: (i) a Hausdorff definably compact definable space is definably normal; (ii) a continuous definable map between Hausdorff locally definably compact definable spaces is definably proper if and only if it is a proper morphism in the category of definable spaces. We give several other characterizations of definably proper, including one involving the existence of limits of definable types. We also prove the basic properties of definably proper maps and the invariance of definably proper (and definably compact) in elementary extensions and o-minimal expansions.

Kategorie tematyczne

• 03C64: Model theory of ordered structures; o-minimality
• 55N30: Sheaf cohomology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 233
• Numer: 1
• Strony: 1-36

Daty

wydano

2016

Twórcy

autor

Mário J. Edmundo

• Universidade Aberta, Rua Braamcamp 90, 1250-052 Lisboa, Portugal
• CMAF Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

autor

Marcello Mamino

• Laboratoire d'Informatique de l'École Polytechnique (LIX), Bâtiment Turing, bureau 2011, 1 rue Honoré d'Estienne d'Orves, Campus de l'École Polytechnique, 91120 Palaiseau, France

autor

Luca Prelli

• CMAF Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal

Identyfikatory

DOI

10.4064/fm96-12-2015