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Jul 19, 2018 at 11:48 comment added Donu Arapura Yes, that's right $\Omega$ should be connected.
Jul 19, 2018 at 11:36 comment added Luke Diahan Thank you for your comment. All we need further is that $\Omega$ is connected so the definition makes sense.
Jul 19, 2018 at 11:31 comment added Donu Arapura No, what happens on the boundary is not relevant for whether $d$ is a metric and for the topology it generates.
Jul 19, 2018 at 1:21 comment added Luke Diahan You mean that these are true for any open, bounded domain $\Omega$ in $\mathbb{C}^{n}$ without any assumption on the smoothness of its boundary.
Jul 18, 2018 at 20:12 history answered Donu Arapura CC BY-SA 4.0