Everywhere dense metrizable subspaces of Corson compacta (Q1081873)

Denote by \({\mathcal E},{\mathcal E}_ 1,{\mathcal E}_ 2,{\mathcal K},{\mathcal K}_ m\) the classes of Eberlein compact spaces, of those X with \(C_ p(X)\) \({\mathcal K}\)-analytic, of those X with \(C_ p(X)\) Lindelöf \(\Sigma\)- spaces, of Corson compact spaces, of Corson compact spaces containing a dense metrizable subspace. Then \[ {\mathcal E}\subset {\mathcal E}_ 1\subset {\mathcal E}_ 2\subset {\mathcal K},\quad {\mathcal E}\subset {\mathcal K}_ m\subset {\mathcal K} \] (all the inclusions are strict). It is proved here that even \({\mathcal E}_ 2\subset {\mathcal K}_ m\) and that the inclusion is strict, that \({\mathcal K}_ m\) is not closed-hereditary and not closed under open continuous images. Also, a simple example showing that \({\mathcal K}-{\mathcal K}_ m\neq \emptyset\) is constructed. The author uses a characterization of spaces from \({\mathcal K}_ m\) by means of \(\sigma\)-disjoint \(\pi\)-bases and adequate families of chains of trees. \{Reviewer's remark: In the English translation, ''complete order'' should read ''well-order'', the first occurring symbols t on lines 5,8 from above on p. 752 should be \(\hat t,\) ''pointwise finite family'' is better to read ''point-finite family''.\}