K-analytic spaces and countable operations in topology.

Necessary and sufficient conditions for a Hausdorff Lindelof space to be embeddable in a Hausdorff K-space are given; thus, an example of a K-analytic space which is not K-Sous1in in any space can be constructed. Conditions under which a 1-1 continuous map preserves K-Borelian sets are given. A general method of construction of a 1-1 continuous map that does not preserve a particular K-Borelian subset is discussed. Necessary and sufficient conditions are given in order that a strongly "tamisable" completely regular space be topologically complete