Topological properties of 𝑞-convex sets

Lupacciolu, Guido

doi:10.1090/S0002-9947-1993-1091708-7

Topological properties of $q$-convex sets
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Trans. Amer. Math. Soc. 337 (1993), 427-435 Request permission

Abstract:

We discuss the topological properties of a certain class of compact sets in a $q$-complete complex manifold $M$. These sets—which we call $q$-convex in $M$—include, for $q = 0$, the $\mathcal {O}(M)$-convex compact sets in a Stein manifold. Then we show applications of the topological results to the subjects of removable singularities for ${\bar \partial _b}$.

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