On Kakutani--Krein and Maeda--Ogasawara spaces

Authors: ZAFER ERCAN, NEŞET ÖZKAN TAN

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^{\infty}(S) spaces, where S is a Stonean space.

Keywords: Riesz space, universal completion, Kakutani--Krein space, Maeda--Ogasawara space

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