J. Aust. Math. Soc.  81 (2006), 49-61
Strict convexity of sets in analytic terms

Leoni Dalla
  The University of Athens
  Department of Mathematics
  Panepistemiopolis 15784
  Athens
  Greece
  ldalla@math.uoa.gr
and
Telemachos Hatziafratis
  The University of Athens
  Department of Mathematics
  Panepistemiopolis 15784
  Athens
  Greece
  thatziaf@math.uoa.gr


Abstract
We compare the geometric concept of strict convexity of open subsets of $\mathbb{R}^n$ with the analytic concept of 2-strict convexity, which is based on the defining functions of the set, and we do this by introducing the class of $2N$-strictly convex sets. We also describe an exhaustion process of convex sets by a sequence of 2-strictly convex sets.
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