Approximately finite-dimensional Banach spaces

AbstractA 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