Definable group extensions in semi-bounded o-minimal structures

摘要

In this note we show: Let R = R,<,+, 0, . . . be a semi-bounded (respectively, linear) o-minimal expansion of an ordered group, and G a group definable in R of linear dimensionm([2]). Then G is a definable extension of a bounded (respectively, definably compact) definable group B by Rm.