Borsukʹs index and pointed movability for projective movable continua

It is shown that each projective movable continuum X is shape dominated by a regularly movable continuum of the same dimension. This has two consequences. First, if the dimension of X is ≤k, k≠2, then X is shape dominated by a continuum in R2k. This answers affirmatively a special case of a question raised by Borsuk, at least as far back as 1975, in all dimensions except dim=2. Second, it implies that such a continuum is pointed movable, again giving an affirmative answer, in a special case, to the old question in shape theory of whether movable continua are always pointed movable.