Abstract
We introduce the concept of Steinness index related to the Stein neighborhood basis. We then show several results: (1) The existence of Steinness index is equivalent to that of strong Stein neighborhood basis. (2) On the Diederich–Fornaess worm domains in particular, we present an explicit formula relating the Steinness index to the well-known Diederich–Fornaess index. (3) The Steinness index is 1 if a smoothly bounded pseudoconvex domain admits finitely many boundary points of infinite type.
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