- The largest class of spaces X having this property is the class of Corson compacta X. Moreover, for the class of Eberlein compacta~, contained in~ f, Arkhangel'skii and Talagran (see [i] and ) proved that if X~, then Cp (X) has type K~ 6. This fact naturally led to picking out the following classes of compacta~ i and~ 2: X~ $1 (X~@ 2), if Cp (X) is a~ fanalytic (LindelDf Z-) space . The assertion that~ C~, was proved by Gul'ko . The inequality@~@ i was established in , $~ in . The long open question of the coincidence of@ i and~ 2 was recently solved negatively by Talagrand . Thus, $ C~ IC@ 2C.~, and all these inclusions are strict.