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J. Sib. Fed. Univ. Math. Phys., 2019, Volume 12, Issue 4, Pages 475–482 (Mi jsfu786)  

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

Abstract: $ \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 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.
The questions were formulated by Yu. B. Zelinsky.

Keywords: strong linear convexity, $ \mathbb C $-convexity, projective convexity, lineal convexity, Fantappie transform, Aizenberg–Martineau duality.

DOI: https://doi.org/10.17516/1997-1397-2019-12-4-475-482

Full text: PDF file (113 kB)
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Bibliographic databases:

UDC: 517.55
Received: 13.01.2019
Received in revised form: 16.02.2019
Accepted: 10.04.2019
Language:

Citation: 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
\Bibitem{Zna19}
\by Sergej~V.~Znamenskij
\paper The closure and the interior of $ \mathbb C$-convex sets
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 4
\pages 475--482
\mathnet{http://mi.mathnet.ru/jsfu786}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-4-475-482}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000483323900010}


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