caa a22 4500 463171527 CHVBK 20180406164814.0 cr unu---uuuuu 170326e20071101xx s 000 0 eng 10.1007/s10998-007-4169-8 doi (NATIONALLICENCE)springer-10.1007/s10998-007-4169-8 Breen Marilyn The University of Oklahoma, 73019, Norman, Oklahoma, USA aut A Krasnosel'skii-type result for planar sets starshaped via orthogonally convex paths [Elektronische Daten] [Marilyn Breen] A Krasnosel'skii-type theorem for compact sets that are starshaped via staircase paths may be extended to compact sets that are starshaped via orthogonally convex paths: Let S be a nonempty compact planar set having connected complement. If every two points of S are visible via orthogonally convex paths from a common point of S, then S is starshaped via orthogonally convex paths. Moreover, the associated kernel Ker S has the expected property that every two of its points are joined in Ker S by an orthogonally convex path. If S is an arbitrary nonempty planar set that is starshaped via orthogonally convex paths, then for each component C of Ker S, every two of points of C are joined in C by an orthogonally convex path. Springer Science+Business Media B.V., 2007 sets starshaped via orthogonally convex paths nationallicence Periodica Mathematica Hungarica Springer Netherlands 55/2(2007-11-01), 169-176 0031-5303 55:2<169 2007 55 10998 https://doi.org/10.1007/s10998-007-4169-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10998-007-4169-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Breen Marilyn The University of Oklahoma, 73019, Norman, Oklahoma, USA aut NATIONALLICENCE 773 0- Periodica Mathematica Hungarica Springer Netherlands 55/2(2007-11-01), 169-176 0031-5303 55:2<169 2007 55 10998 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer