The closure and the interior of $ \mathbb C$-convex sets
Sergej V. Znamenskij
Ailamazyan Program Systems Institute of RAS, Peter the First Street, 4, Veskovo village, Pereslavl area, Yaroslavl region, 152021, Russia
$ \mathbb C $-convexity of the closure, interiors and their lineal convexity are considered for $ \mathbb C $-convex sets under additional conditions of boundedness and nonempty interiors. The following questions on closure and the interior of $\mathbb C $-convex sets were tackled
The questions were formulated by Yu. B. Zelinsky.
- The closure of a bounded $ \mathbb C $-convex domain may not be lineally-convex.
- The closure of a non-empty interior of a $ \mathbb C $-convex compact in $ \mathbb C^n $ may not coincide with the original compact.
- The interior of the closure of a bounded $ \mathbb C $-convex domain always coincides with the domain itself.
strong linear convexity, $ \mathbb C $-convexity, projective convexity, lineal convexity, Fantappie transform, Aizenberg–Martineau duality.
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Received in revised form: 16.02.2019
Sergej V. Znamenskij, “The closure and the interior of $ \mathbb C$-convex sets”, J. Sib. Fed. Univ. Math. Phys., 12:4 (2019), 475–482
Citation in format AMSBIB
\paper The closure and the interior of $ \mathbb C$-convex sets
\jour J. Sib. Fed. Univ. Math. Phys.
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