  We study definably complete locally o-minimal expansions of ordered groups in
this paper. A definable continuous function defined on a closed, bounded and
definable set behave like a continuous function on a compact set. We
demonstrate uniform continuity of a definable continuous function on a closed,
bounded and definable set and Arzela-Ascoli-type theorem. We propose a notion
of special submanifolds with tubular neighborhoods and show that any definable
set is decomposed into finitely many special submanifolds with tubular
neighborhoods.
