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In this paper we construct open Stein neighbourhoods of compact sets of theform $A\cup K$ in a complex space, where $K$ is a compact holomorphicallyconvex set, $A$ is a compact complex curve with boundary $bA$ of class$\mathscr C^2$ which may intersect $K$, and $A\cap K$ is $\mathscrO(A)$-convex.

Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets