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Apr 27, 2013 at 7:41 comment added AlexE I asked the above question as a separate one: mathoverflow.net/questions/128901
Apr 26, 2013 at 12:46 comment added AlexE Thanks for your answer! But I can't figure out what you mean by "since the inductive tensor product does not commute with direct limits". I'm now especially interested in the following case: If $X$ is a metric space, denote by $C_u(X)$ the $C^\ast$-algebra of all bounded, uniformly continuous functions on $X$ (with the sup-norm). Do we have $C_u(X_1 \times X_2) = C_u(X_1) \widehat{\otimes} C_u(X_2)$?
Jan 31, 2013 at 15:58 history answered Peter Michor CC BY-SA 3.0