Advances on Ricceri's Most Famous Conjecture
New advances towards a (positive) solution to Ricceri's (most famous) Conjecture are presented. One of these advances consists of showing that a totally anti-proximinal absolutely convex subset of a vector space is linearly open. We also prove that if every totally anti-proximinal convex subset...
Gespeichert in:
| Veröffentlicht in: | Filomat 2015-01, Vol.29 (4), p.829-838 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 838 |
|---|---|
| container_issue | 4 |
| container_start_page | 829 |
| container_title | Filomat |
| container_volume | 29 |
| creator | García-Pacheco, F. J. Hill, J. R. |
| description | New advances towards a (positive) solution to Ricceri's (most famous) Conjecture are presented. One of these advances consists of showing that a totally anti-proximinal absolutely convex subset of a vector space is linearly open. We also prove that if every totally anti-proximinal convex subset of a vector space is linearly open then Ricceri's Conjecture holds true. Finally we demonstrate that the concept of total anti-proximinality does not make sense in the scope of pseudo-normed spaces. |
| doi_str_mv | 10.2298/FIL1504829G |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_2298_FIL1504829G</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>24898164</jstor_id><sourcerecordid>24898164</sourcerecordid><originalsourceid>FETCH-LOGICAL-c250t-4f109b29c1382dcdd504235fa005b533dda2f67b49d64f18ecd93ef016d8bac03</originalsourceid><addsrcrecordid>eNpNz0tLxDAUBeAgCtbRlWuhOxdavbl5TLIcih0HKoLouqR5QIszkaQj-O-tjIirs_k4nEPIJYU7RK3um01LBXCFen1ECuQgK9CMHZMCmOCVoApOyVnOIwBHyZcFuV25T7OzPpdxV74M1vo0XOfyKeapbMw27nNZx93o7bRP_pycBPOe_cVvLshb8_BaP1bt83pTr9rKooCp4oGC7lFbyhQ669w8CZkIBkD0gjHnDAa57Ll2crbKW6eZD0ClU72xwBbk5tBrU8w5-dB9pGFr0ldHofs52v07Ouurgx7zFNMfRa60opKzb24FTi0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Advances on Ricceri's Most Famous Conjecture</title><source>JSTOR Mathematics & Statistics</source><source>JSTOR Archive Collection A-Z Listing</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>García-Pacheco, F. J. ; Hill, J. R.</creator><creatorcontrib>García-Pacheco, F. J. ; Hill, J. R.</creatorcontrib><description>New advances towards a (positive) solution to Ricceri's (most famous) Conjecture are presented. One of these advances consists of showing that a totally anti-proximinal absolutely convex subset of a vector space is linearly open. We also prove that if every totally anti-proximinal convex subset of a vector space is linearly open then Ricceri's Conjecture holds true. Finally we demonstrate that the concept of total anti-proximinality does not make sense in the scope of pseudo-normed spaces.</description><identifier>ISSN: 0354-5180</identifier><identifier>EISSN: 2406-0933</identifier><identifier>DOI: 10.2298/FIL1504829G</identifier><language>eng</language><publisher>Faculty of Sciences and Mathematics, University of Niš</publisher><subject>Convexity ; Topological spaces ; Topological vector spaces ; Unit ball ; Vector spaces</subject><ispartof>Filomat, 2015-01, Vol.29 (4), p.829-838</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/24898164$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/24898164$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,4021,27921,27922,27923,58015,58019,58248,58252</link.rule.ids></links><search><creatorcontrib>García-Pacheco, F. J.</creatorcontrib><creatorcontrib>Hill, J. R.</creatorcontrib><title>Advances on Ricceri's Most Famous Conjecture</title><title>Filomat</title><description>New advances towards a (positive) solution to Ricceri's (most famous) Conjecture are presented. One of these advances consists of showing that a totally anti-proximinal absolutely convex subset of a vector space is linearly open. We also prove that if every totally anti-proximinal convex subset of a vector space is linearly open then Ricceri's Conjecture holds true. Finally we demonstrate that the concept of total anti-proximinality does not make sense in the scope of pseudo-normed spaces.</description><subject>Convexity</subject><subject>Topological spaces</subject><subject>Topological vector spaces</subject><subject>Unit ball</subject><subject>Vector spaces</subject><issn>0354-5180</issn><issn>2406-0933</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNpNz0tLxDAUBeAgCtbRlWuhOxdavbl5TLIcih0HKoLouqR5QIszkaQj-O-tjIirs_k4nEPIJYU7RK3um01LBXCFen1ECuQgK9CMHZMCmOCVoApOyVnOIwBHyZcFuV25T7OzPpdxV74M1vo0XOfyKeapbMw27nNZx93o7bRP_pycBPOe_cVvLshb8_BaP1bt83pTr9rKooCp4oGC7lFbyhQ669w8CZkIBkD0gjHnDAa57Ll2crbKW6eZD0ClU72xwBbk5tBrU8w5-dB9pGFr0ldHofs52v07Ouurgx7zFNMfRa60opKzb24FTi0</recordid><startdate>20150101</startdate><enddate>20150101</enddate><creator>García-Pacheco, F. J.</creator><creator>Hill, J. R.</creator><general>Faculty of Sciences and Mathematics, University of Niš</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20150101</creationdate><title>Advances on Ricceri's Most Famous Conjecture</title><author>García-Pacheco, F. J. ; Hill, J. R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c250t-4f109b29c1382dcdd504235fa005b533dda2f67b49d64f18ecd93ef016d8bac03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Convexity</topic><topic>Topological spaces</topic><topic>Topological vector spaces</topic><topic>Unit ball</topic><topic>Vector spaces</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>García-Pacheco, F. J.</creatorcontrib><creatorcontrib>Hill, J. R.</creatorcontrib><collection>CrossRef</collection><jtitle>Filomat</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>García-Pacheco, F. J.</au><au>Hill, J. R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Advances on Ricceri's Most Famous Conjecture</atitle><jtitle>Filomat</jtitle><date>2015-01-01</date><risdate>2015</risdate><volume>29</volume><issue>4</issue><spage>829</spage><epage>838</epage><pages>829-838</pages><issn>0354-5180</issn><eissn>2406-0933</eissn><abstract>New advances towards a (positive) solution to Ricceri's (most famous) Conjecture are presented. One of these advances consists of showing that a totally anti-proximinal absolutely convex subset of a vector space is linearly open. We also prove that if every totally anti-proximinal convex subset of a vector space is linearly open then Ricceri's Conjecture holds true. Finally we demonstrate that the concept of total anti-proximinality does not make sense in the scope of pseudo-normed spaces.</abstract><pub>Faculty of Sciences and Mathematics, University of Niš</pub><doi>10.2298/FIL1504829G</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0354-5180 |
| ispartof | Filomat, 2015-01, Vol.29 (4), p.829-838 |
| issn | 0354-5180 2406-0933 |
| language | eng |
| recordid | cdi_crossref_primary_10_2298_FIL1504829G |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals |
| subjects | Convexity Topological spaces Topological vector spaces Unit ball Vector spaces |
| title | Advances on Ricceri's Most Famous Conjecture |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T11%3A10%3A59IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Advances%20on%20Ricceri's%20Most%20Famous%20Conjecture&rft.jtitle=Filomat&rft.au=Garc%C3%ADa-Pacheco,%20F.%20J.&rft.date=2015-01-01&rft.volume=29&rft.issue=4&rft.spage=829&rft.epage=838&rft.pages=829-838&rft.issn=0354-5180&rft.eissn=2406-0933&rft_id=info:doi/10.2298/FIL1504829G&rft_dat=%3Cjstor_cross%3E24898164%3C/jstor_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=24898164&rfr_iscdi=true |