Visible shorelines for unions of islands
For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a...
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| Autor*in: |
Breen, Marilyn [verfasserIn] |
|---|
| Format: |
E-Artikel |
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| Erschienen: |
Walter de Gruyter GmbH & Co. KG ; 2011 |
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| Schlagwörter: |
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| Anmerkung: |
© de Gruyter 2011 |
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| Umfang: |
6 |
| Reproduktion: |
Walter de Gruyter Online Zeitschriften |
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| Übergeordnetes Werk: |
Enthalten in: Advances in geometry - Berlin [u.a.] : de Gruyter, 2001, 11(2011), 3 vom: 09. Juni, Seite 557-562 |
| Übergeordnetes Werk: |
volume:11 ; year:2011 ; number:3 ; day:09 ; month:06 ; pages:557-562 ; extent:6 |
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10.1515/advgeom.2011.013 |
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| 520 | |a For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn. | ||
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10.1515/advgeom.2011.013 doi artikel_Grundlieferung.pp (DE-627)NLEJ246368357 DE-627 ger DE-627 rakwb Breen, Marilyn verfasserin aut Visible shorelines for unions of islands Walter de Gruyter GmbH & Co. KG 2011 6 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2011 For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn. Walter de Gruyter Online Zeitschriften Visible shorelines Enthalten in Advances in geometry Berlin [u.a.] : de Gruyter, 2001 11(2011), 3 vom: 09. Juni, Seite 557-562 (DE-627)NLEJ248234919 (DE-600)2043066-8 1615-7168 nnns volume:11 year:2011 number:3 day:09 month:06 pages:557-562 extent:6 https://doi.org/10.1515/advgeom.2011.013 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 11 2011 3 09 06 557-562 6 |
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10.1515/advgeom.2011.013 doi artikel_Grundlieferung.pp (DE-627)NLEJ246368357 DE-627 ger DE-627 rakwb Breen, Marilyn verfasserin aut Visible shorelines for unions of islands Walter de Gruyter GmbH & Co. KG 2011 6 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2011 For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn. Walter de Gruyter Online Zeitschriften Visible shorelines Enthalten in Advances in geometry Berlin [u.a.] : de Gruyter, 2001 11(2011), 3 vom: 09. Juni, Seite 557-562 (DE-627)NLEJ248234919 (DE-600)2043066-8 1615-7168 nnns volume:11 year:2011 number:3 day:09 month:06 pages:557-562 extent:6 https://doi.org/10.1515/advgeom.2011.013 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 11 2011 3 09 06 557-562 6 |
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10.1515/advgeom.2011.013 doi artikel_Grundlieferung.pp (DE-627)NLEJ246368357 DE-627 ger DE-627 rakwb Breen, Marilyn verfasserin aut Visible shorelines for unions of islands Walter de Gruyter GmbH & Co. KG 2011 6 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2011 For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn. Walter de Gruyter Online Zeitschriften Visible shorelines Enthalten in Advances in geometry Berlin [u.a.] : de Gruyter, 2001 11(2011), 3 vom: 09. Juni, Seite 557-562 (DE-627)NLEJ248234919 (DE-600)2043066-8 1615-7168 nnns volume:11 year:2011 number:3 day:09 month:06 pages:557-562 extent:6 https://doi.org/10.1515/advgeom.2011.013 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 11 2011 3 09 06 557-562 6 |
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10.1515/advgeom.2011.013 doi artikel_Grundlieferung.pp (DE-627)NLEJ246368357 DE-627 ger DE-627 rakwb Breen, Marilyn verfasserin aut Visible shorelines for unions of islands Walter de Gruyter GmbH & Co. KG 2011 6 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2011 For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn. Walter de Gruyter Online Zeitschriften Visible shorelines Enthalten in Advances in geometry Berlin [u.a.] : de Gruyter, 2001 11(2011), 3 vom: 09. Juni, Seite 557-562 (DE-627)NLEJ248234919 (DE-600)2043066-8 1615-7168 nnns volume:11 year:2011 number:3 day:09 month:06 pages:557-562 extent:6 https://doi.org/10.1515/advgeom.2011.013 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 11 2011 3 09 06 557-562 6 |
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10.1515/advgeom.2011.013 doi artikel_Grundlieferung.pp (DE-627)NLEJ246368357 DE-627 ger DE-627 rakwb Breen, Marilyn verfasserin aut Visible shorelines for unions of islands Walter de Gruyter GmbH & Co. KG 2011 6 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © de Gruyter 2011 For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn. Walter de Gruyter Online Zeitschriften Visible shorelines Enthalten in Advances in geometry Berlin [u.a.] : de Gruyter, 2001 11(2011), 3 vom: 09. Juni, Seite 557-562 (DE-627)NLEJ248234919 (DE-600)2043066-8 1615-7168 nnns volume:11 year:2011 number:3 day:09 month:06 pages:557-562 extent:6 https://doi.org/10.1515/advgeom.2011.013 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 11 2011 3 09 06 557-562 6 |
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For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn. © de Gruyter 2011 |
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For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn. © de Gruyter 2011 |
| abstract_unstemmed |
For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn. © de Gruyter 2011 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ246368357</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220820022040.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220814s2011 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/advgeom.2011.013</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">artikel_Grundlieferung.pp</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ246368357</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Breen, Marilyn</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Visible shorelines for unions of islands</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="b">Walter de Gruyter GmbH & Co. KG</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">6</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© de Gruyter 2011</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">For positive integers m and n, let S1, . . . , Sn be nonempty sets, each having a subset of at most m labeled points, and let P be a nonempty set. Assume that a subset of each point p of P is associated with some (visibility) subset V(p) of S1 ∪ ⋯ ∪ Sn. We ask the following question, motivated by a result of Valentine: When will there exist a set of labeled points s1, . . . , sn, si in Si, 1 ≤ i ≤ n, such that each V(p) set contains at least one of the si points? Three results are given here. The first concerns the case for general Si sets. The second concerns the case in which the Si sets are simple arcs and V(p) ∩ Si is connected for each p and each i. The third result interprets the Si sets as compact, convex islands in the plane and interprets the V(p) sets as visible shorelines of Si ∪ ⋯ ∪ Sn.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">Walter de Gruyter Online Zeitschriften</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Visible shorelines</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Advances in geometry</subfield><subfield code="d">Berlin [u.a.] : de Gruyter, 2001</subfield><subfield code="g">11(2011), 3 vom: 09. Juni, Seite 557-562</subfield><subfield code="w">(DE-627)NLEJ248234919</subfield><subfield code="w">(DE-600)2043066-8</subfield><subfield code="x">1615-7168</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:11</subfield><subfield code="g">year:2011</subfield><subfield code="g">number:3</subfield><subfield code="g">day:09</subfield><subfield code="g">month:06</subfield><subfield code="g">pages:557-562</subfield><subfield code="g">extent:6</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/advgeom.2011.013</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-DGR</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">11</subfield><subfield code="j">2011</subfield><subfield code="e">3</subfield><subfield code="b">09</subfield><subfield code="c">06</subfield><subfield code="h">557-562</subfield><subfield code="g">6</subfield></datafield></record></collection>
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