This is an announcement for the paper "Topological properties of the continuous function spaces on some ordered compacta" by Wieslaw Kubis, Anibal Molto, and Stanimir Troyanski. Abstract: Some new classes of compacta $K$ are considered for which $C(K)$ endowed with the pointwise topology has a countable cover by sets of small local norm--diameter. Archive classification: math.FA math.GN Mathematics Subject Classification: 46B26, 03G10 Remarks: 11 pages Submitted from: kubis@math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1302.0829 or http://arXiv.org/abs/1302.0829