Metric spaces are *isometric* if there exists a bijective isometry between them.

Is there a standard notation for this, along the same lines as $X\approx Y$ for homeomorphic spaces and $X\simeq Y$ for homotopy equivalent spaces?

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Metric spaces are *isometric* if there exists a bijective isometry between them.

Is there a standard notation for this, along the same lines as $X\approx Y$ for homeomorphic spaces and $X\simeq Y$ for homotopy equivalent spaces?

categoryis clear in the context. $\endgroup$ – Martin Brandenburg Oct 28 '11 at 9:18