Uniformly continuous 1-1 functions on ordered fields not mapping interior to interior

In an earlier work we showed that for ordered fields f not isomorphic tothe reals r, there are continuous 1-1 functions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 functions not mapping interior to interior. in particular, the minimal non-archimedean ordered field q(x), as well as ordered laurent series fields with coefficients in an ordered field accommodate such pathological functions.