Selections, Paracompactness and Compactness
2000 Mathematics Subject Classification: 54C60, 54C65, 54D20, 54D30. In the present paper the Lindelöf number and the degree of compactness of spaces and of the cozero-dimensional kernel of paracompact spaces are characterized in terms of selections of lower semi-continuous closed-valued mappings into complete metrizable (or discrete) spaces.