We present deep I and z imaging of the colour-selected cluster RzCS 052 and study the color-magnitude relation of this cluster, its scatter, the morphological distribution on the red sequence, the luminosity and stellar mass functions of red galaxies and the cluster blue fraction. We find that the stellar populations of early type galaxies in this cluster are uniformly old and that their luminosity function does not show any sign of evolution other than the passive evolution of their stellar populations. We rule out a significant contribution from mergers in the buildup of the red sequence of RzCS 052. The cluster has a large (~30%) blue fraction and and we infer that the evolution of the blue galaxies is faster than an exponentially declining star formation model and that these objects have probably experienced starburst episodes. Mergers are unlikely to be the driver of the observed colour evolution, because of the measured constancy of the mass function, as derived from near-infrared photometry of 32 clusters, including RzCS 052, presented in a related paper. Mechanisms with clustercentric radial dependent efficiencies are disfavored as well, because of the observed constant blue fraction with clustercentric distance.
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