On definably proper maps

Mário J. Edmundo, Marcello Mamino, and Luca Prelli. "On definably proper maps." Fundamenta Mathematicae 233.1 (2016): 1-36. <http://eudml.org/doc/282893>.

@article{MárioJ2016,
abstract = {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.},
author = {Mário J. Edmundo, Marcello Mamino, Luca Prelli},
journal = {Fundamenta Mathematicae},
keywords = {o-minimal structures; definably proper},
language = {eng},
number = {1},
pages = {1-36},
title = {On definably proper maps},
url = {http://eudml.org/doc/282893},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Mário J. Edmundo
AU - Marcello Mamino
AU - Luca Prelli
TI - On definably proper maps
JO - Fundamenta Mathematicae
PY - 2016
VL - 233
IS - 1
SP - 1
EP - 36
AB - 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.
LA - eng
KW - o-minimal structures; definably proper
UR - http://eudml.org/doc/282893
ER -