Properties of Banach spaces related to projectivity (Q1092389)

Let \(Ban_ 1\) denote the category of Banach spaces with morphisms as bounded linear maps of norm \(\leq 1\). The author in this note gives an analogue of the well-known results of Gleason (in the category of compact Hausdorff spaces and continuous maps). He defines the analogues of ``projective objects'' and extremally disconnected spaces in this setting. But in \(Ban_ 1\) ``extremally disconnectedness'' does not appear as the intrinsic characterisation of projective objects.