Linear operators with compact supports, probability measures and Milyutin maps

The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for zero-dimensional spaces in terms of regular extension operators having compact supports. Milyutin maps are also considered and it is established that some topological properties, like paracompactness, metrizability and k-metrizability, are preserved under Milyutin maps.Comment: 26 page

Skeletally generated spaces and absolutes

Some properties of skelatally generated spaces are established. In particular, it is shown that any compactum co-absolute to a $\kappa$-metrizable compactum is skeletally generated. We also prove that a compactum $X$ is skeletally generated if and only if its superextension $\lambda X$ is skeletally Dugundji and raise some natural questions.Comment: 9 page