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Mar 3, 2023 at 16:32 comment added Doug Liu Dea @user3566, what is your definition of "holomorphically convex"? If you mean $H(X)$-convexity defined in p.472 of Rossi's paper you cited, then an annulus in $\mathbb{C}$ possesses a fundamental system of neighbourhoods which are Stein opens, while $K$ is not $H(\mathbb{C})$-convex, see p.477 loc.cit.
Nov 28, 2011 at 12:56 vote accept user3566
Nov 28, 2011 at 12:56 answer added user3566 timeline score: 2
Nov 9, 2010 at 19:47 history asked user3566 CC BY-SA 2.5