مشخصات پژوهش

In o-minimal structures, every cell is definably connected and every definable set is a finite union of its definably connected component. In this note, after introducing the notation of pseudo definably connectedness and pseudo definably path connectedness in M, we show that strong cells in M are pseudo definably connected, so every definable set in M has finitely many pseudo definably connected components. Moreover, we prove that every pseudo definably connected definable set is a pseudo definably path connected.