Abstract
Let S be a simply connected orthogonal polygon in the plane. A family of examples will establish the following result. For every n ≥ 2, there exists no Krasnosel’skii number h(n) which satisfies this property: If every h(n) points of S are visible via staircase n-paths from a common point, then S is starshaped via staircase n-paths.
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Breen, M.: A Krasnosel’skii theorem for orthogonal polygons starshaped via staircase (n + 1)-paths (submitted) (2009)
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Breen, M. A family of examples showing that no Krasnosel’skii number exists for orthogonal polygons starshaped via staircase n-paths. J. Geom. 94, 1–6 (2009). https://doi.org/10.1007/s00022-009-0007-5
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DOI: https://doi.org/10.1007/s00022-009-0007-5