It has recently been solved by K.Iwas&wa C1J the problem of linearization oΓ an abstract groups* In this note we shall investigate the problem of linearization of topological βroups. We say that a topcloglcal group G can be linearizecj, if we can introduce such a linear order in G that G becomes a linearly ordered group and that the topology of G is equivalent to the intrinsic topology by this order• Then, using the concept of an ordered ring we characterize the field of real numbers and the ring of integers.