  Some conceptual issues concerning $f(T)$ theories --a family of modified
gravity theories based on absolute parallelism-- are analyzed. Due to the lack
of local Lorentz invariance, the autoparallel frames satisfying the field
equations are evasive to an \emph{a priori} physical understanding. We
exemplify this point by working out the vierbein (tetrad) fields for closed and
open Friedmann-Robertson-Walker cosmologies.
