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Spindle starshaped sets

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Abstract

In this paper, spindle starshaped sets are introduced and investigated, which apart from normalization form an everywhere dense subfamily within the family of starshaped sets. We focus on proving spindle starshaped analogues of recent theorems of Bobylev, Breen, Toranzos, and Zamfirescu on starshaped sets. Finally, we consider the problem of guarding treasures in an art gallery (in the traditional linear way as well as via spindles).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

    Károly Bezdek

  2. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    Károly Bezdek

  3. Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary

    Márton Naszódi

Authors
  1. Károly Bezdek
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  2. Márton Naszódi
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Correspondence to Márton Naszódi.

Additional information

Károly Bezdek Partially supported by a Natural Sciences and Engineering Research Council of Canada Discovery Grant.

Márton Naszódi Partially supported by the Hung. Nat. Sci. Found. (OTKA) grants: K72537 and PD104744 and by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

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Bezdek, K., Naszódi, M. Spindle starshaped sets. Aequat. Math. 89, 803–819 (2015). https://doi.org/10.1007/s00010-014-0271-9

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  • DOI: https://doi.org/10.1007/s00010-014-0271-9

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