Coverings by open cells
M\'ario J. Edmundo, Pantelis Eleftheriou, Luca Prelli
TL;DR
This paper proves that in semi-bounded o-minimal structures, every non-empty open definable set can be expressed as a finite union of open cells, simplifying their geometric understanding.
Contribution
It establishes a new structural result about open definable sets in semi-bounded o-minimal structures, showing they are finite unions of open cells.
Findings
Non-empty open definable sets are finite unions of open cells
The result applies specifically to semi-bounded o-minimal expansions of ordered groups
Simplifies the geometric analysis of definable sets in these structures
Abstract
We prove that in a semi-bounded o-minimal expansion of an ordered group every non-empty open definable set is a finite union of open cells.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Advanced Algebra and Logic