Approximative Weak Compactness

Approximative weak compactness is studied for problems of min-and max-approximation. This leads naturally to certain 'special points' of approximation theory, namely the spaces characterizable in terms of approximative weak compactness type properties for various classical problems of approximation theory. Among these 'special points' appear the Kadec-Klee spaces (KK), as well as the wDO-, VDS-, MAT-spaces, and the spaces in the class (wDO) boolean AND (R). Bibliography: 29 titles.