Abstract
A Banach space is said to be approximately finite-dimensional if it has a nonstandard hull linearly isometric to a hyperfinite-dimensional Banach space or, equivalently, if an ultrapower is linearly isometric to an ultraproduct of finite-dimensional spaces. It is shown that the space C( K) of continuous functions on a compact Hausdorff space K is approximately finite-dimensional if and only if K is totally disconnected and contains a dense subset of isolated points.
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