On Kakutani Krein and Maeda Ogasawara spaces

Abstract

: Let E be an Archimedean Riesz space. It is shown that the Kakutani Krein space of the center of the Dedekind completion of E and the Maeda Ogasawara space of E are homeomorphic. By applying this, we can reprove a Banach Stone type theorem for C ∞(S) spaces, where S is a Stonean space.