Clarification for definition of admissible: $\Delta\in (K)$

36 Views Asked by At

I am reading through the following book: E.M. Nikishin, V.N. Sorokin: Rational Approximations and Orthogonality, Translations of Mathematical Monographs, vol. 92, Amer. Math. Soc., Provindence RI, 1991.

At page 183, the definition of an admissible set is given:

Let G be a domain in $\overline{\mathbb{C}}=\mathbb{C}\cup \infty$ that contains the point at infinity, and let $\Delta=\partial G$ be its boundary. If $\Delta \in (\mathrm{K})$, we say that $\Delta$ is admissible.

I don't recall reading anything about this set $(\mathrm{K})$, so I'm stuck at this definition. Does it simply mean that $\Delta$ is compact? Looking online for an explanation didn't work, since the word 'admissible' is apparently used in many different contexts.