Definable curve selection in weakly o-minimal structures

In this note, we examine the existence of a definable curve selection in non-valuational weakly o-minimal expansion of ordered groups. Definable curve selections in the o-minimal expansions of ordered groups play a role similar to that of sequences in Euclidean spaces which existence of those proved by van den Dries. Indeed, we show that every non-valuational weakly o-minimal expansion of ordered groups has a property like the definable curve selection in o-minimal setting