Resolvability of A-, CA- and PCA-sets in compacta

The resolvability of A-sets of uncountable dispersion character and CA-sets and PCA-sets, without isolated points in Hausdorff compacta is proved. Examples of a Hausdorff countably compact irresolvable space, a Hausdorff σ-compact irresolvable space of uncountable dispersion character and two σ-compact Tychonoff spaces whose difference is an irresolvable space of uncountable dispersion character are constructed. A number of problems are raised.