  We study compact spaces which are obtained from metric compacta by iterating
the operation of inverse limit of continuous sequences of retractions. We
denote this class by R. Allowing continuous images in the definition of class
R, one obtains a strictly larger class, which we denote by RC. We show that
every space in class RC is either Corson compact or else contains a copy of the
ordinal segment $[0,\omega_1]$. This improves a result of Kalenda, where the
same was proved for the class of continuous images of Valdivia compacta. We
prove that spaces in class R do not contain cutting P-points (see the
definition below), which provides a tool for finding spaces in RC minus R.
Finally, we study linearly ordered spaces in class RC. We prove that scattered
linearly ordered compacta belong to RC and we characterize those ones which
belong to R. We show that there are only 5 types (up to order isomorphism) of
connected linearly ordered spaces in class R and all of them are Valdivia
compact. Finally, we find a universal pre-image for the class of all linearly
ordered Valdivia compacta.
