Abstract:We extend Zaj\'\i{}\v{c}ek's theorem from [Za] about points of singlevaluedness of monotone operators on Asplund spaces. Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a $\sigma $-cone supported set.
Keywords: Asplund spaces, GSG spaces, monotone operators, countable dentability
AMS Subject Classification: 47H05, 46B20