Original scientific paper

https://doi.org/10.21857/y26keclz69

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

Mourad Berraho ; Department of Mathematics, Ibn Tofail University, Faculty of Sciences, Kenitra, Morocco

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.

Keywords

Coordinate projection; Grothendieck rings; definably complete locally o-minimal expansion of a densely linearly ordered abelian group

Hrčak ID:

307482

URI

https://hrcak.srce.hr/307482

Publication date:

25.8.2023.

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