LOCALLY O-MINIMAL STRUCTURES WITH TAME TOPOLOGICAL PROPERTIES

Abstract We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly expansions the second kind densely linearly ordered abelian groups. derive basic dimension a set definable in including addition property, which is equality for maps whose fibers are equi-dimensional. A decomposition theorem into quasi-special submanifolds also demonstrated.