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A note on generic subsets of definable groups

100%

Edmundo M., Terzo G.

Fundamenta Mathematicae

2011

tom 215

nr 1

53-65

We generalize the theory of generic subsets of definably compact definable groups to arbitrary o-minimal structures. This theory is a crucial part of the solution to Pillay's conjecture connecting definably compact definable groups with Lie groups.

On definably proper maps

81%

Edmundo M., Mamino M., Prelli L.

Fundamenta Mathematicae

2016

tom 233

nr 1

1-36

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.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Edmundo M.

1 Mamino M.

1 Prelli L.

1 Terzo G.

1 2016

1 2011

Wyniki wyszukiwania

A note on generic subsets of definable groups

On definably proper maps