A note on linear mappings between function spaces
Arhangel’skiǐ proved that if and are completely regular spaces such that and are linearly homeomorphic, then is pseudocompact if and only if is pseudocompact. In addition he proved the same result for compactness, -compactness and realcompactness. In this paper we prove that if is a continuous linear surjection, then is pseudocompact provided is and if is a continuous linear injection, then is pseudocompact provided is. We also give examples that both statements do not hold...