THE ROSAT BRIGHTEST CLUSTER SAMPLE (BCS) - THE CLUSTER X-RAY LUMINOSITY FUNCTION WITHIN Z=0.3

We present and discuss the X-ray luminosity function (XLF) of the ROSA T Brightest Cluster sample (BCS), an X-ray flux limited sample of clus ters of galaxies in the northern hemisphere compiled from ROSAT All-Sk y Survey data. The BCS allows the local cluster XLF to be determined w ith unprecedented accuracy over almost three decades in X-ray luminosi ty and provides an important reference for searches for cluster evolut ion at higher redshifts. We find the significance of evolution in both the XLF amplitude and in the characteristic cluster luminosity L-x t o be less than 1.8 sigma within the redshift range covered by our samp le thereby disproving previous claims of strong evolution within z les s than or similar to 0.2.