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- Title
THE SURJECTIVITY AND THE CONTINUITY OF DEFINABLE FUNCTIONS IN SOME DEFINABLY COMPLETE LOCALLY O-MINIMAL EXPANSIONS AND THE GROTHENDIECK RING OF ALMOST O-MINIMAL STRUCTURES.
- Authors
BERRAHO, MOURAD
- Abstract
In this paper, we first show that in a definably complete locally o-minimal expansion of an ordered abelian group (M, <, +, 0, ...) and for a definable subset X ⊆ Mn which is closed and bounded in the last coordinate such that the set πn−1(X) is open, the mapping πn−1 is surjective from X to Mn−1, where πn−1 denotes the coordinate projection onto the first n − 1 coordinates. Afterwards, we state some of its consequences. Also we show that the Grothendieck ring of an almost o-minimal expansion of an ordered divisible abelian group which is not o-minimal is null. Finally, we study the continuity of the derivative of a given definable function in some ordered structures.
- Subjects
GROTHENDIECK groups; ABELIAN groups; CONTINUITY; K-theory; MONOIDS
- Publication
Rad HAZU: Matematicke Znanosti, 2023, Vol 27, p1
- ISSN
1845-4100
- Publication type
Article
- DOI
10.21857/y26keclz69