This question is related to [these][1] [two][2].

Let $X\subset \mathbb{C}^{n}$ be a bounded domain. I am interested in the following **property**: there is a sequence of continuous maps $\varphi_n:\overline{X}\to X$ which are holomorphic on $X$ and such that $\varphi_n(x)\to \varphi(x)$, for every $x \in X$. Every convex domain has this property.

>If $n=1$ is this **property** equivalent to $X$ being a Jordan domain?

>If $n>1$ and $X$ is pseudoconvex what are some sufficient conditions on $X$ (other than convexity) so that it has this **property**?

  [1]: https://mathoverflow.net/questions/331172/a-continuous-bi-lipschitz-shrinking-of-a-domain-into-a-compact-subset
  [2]: https://mathoverflow.net/questions/354304/density-of-continuous-functions-to-interior-in-set-of-all-continuous-functions/354358#354358