OPEN CELL PROPERTY IN WEAKLY O-MINIMAL STRUCTURES

Source abstract

In this paper, we prove that every definable bounded open set is a union of finitely many open strong cells in a non-valuational weakly $o$-minimal expansion of a real closed field. Furthermore, we show that a non-valuational weakly $o$-minimal expansion of an ordered group has the open cell property if and only if its canonical $o$-minimal extension is semi-bounded.