Graph intersection property
<p style="font-style: normal;"><span style="font-family: DejaVu Sans,sans-serif;">A pair <em>(X,Y) </em>of topological spaces X and Y<em> </em>is said to have the graph intersection property provided that for each continuous function <em>...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Università degli Studi di Catania
1992-05-01
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| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/577 |
| _version_ | 1811191914865623040 |
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| author | J. J. Charatonik K. Omiljanowski Biagio Ricceri |
| author_facet | J. J. Charatonik K. Omiljanowski Biagio Ricceri |
| author_sort | J. J. Charatonik |
| collection | DOAJ |
| description | <p style="font-style: normal;"><span style="font-family: DejaVu Sans,sans-serif;">A pair <em>(X,Y) </em>of topological spaces X and Y<em> </em>is said to have the graph intersection property provided that for each continuous function <em>g: XY</em>, if a connected subset of<em> X Y </em>projects onto the whole <em>Y</em>, then it intersect the graph of <em>g</em>. Various relations between this and other known properties related to mapping theory are studied.</span></p> <p style="font-style: normal;"><span style="font-family: DejaVu Sans,sans-serif;">In particular, it is proved that: 1) if a space <em>X</em> is completely regular and a space <em>Y </em>is an arcwise connected metric continuum distinct from an arc, then the pair <em>(X,Y)</em> has the graph intersection property if and only if <em>X</em> is hereditary disconnected; 2) if a connected space <em>Y</em> is fixed, then the graph intersection property holds for every pair <em>(X,Y)</em> if and only if there is a closed linear order on <em>Y</em> with minimal and maximal elements. Related results are obtained.</span></p> |
| first_indexed | 2024-04-11T23:43:54Z |
| format | Article |
| id | doaj.art-ec814b1b44c94f088013b3224800bfd7 |
| institution | Directory Open Access Journal |
| issn | 0373-3505 2037-5298 |
| language | English |
| last_indexed | 2024-04-11T23:43:54Z |
| publishDate | 1992-05-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| series | Le Matematiche |
| spelling | doaj.art-ec814b1b44c94f088013b3224800bfd72022-12-22T03:56:43ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52981992-05-01471103115544Graph intersection propertyJ. J. CharatonikK. OmiljanowskiBiagio Ricceri<p style="font-style: normal;"><span style="font-family: DejaVu Sans,sans-serif;">A pair <em>(X,Y) </em>of topological spaces X and Y<em> </em>is said to have the graph intersection property provided that for each continuous function <em>g: XY</em>, if a connected subset of<em> X Y </em>projects onto the whole <em>Y</em>, then it intersect the graph of <em>g</em>. Various relations between this and other known properties related to mapping theory are studied.</span></p> <p style="font-style: normal;"><span style="font-family: DejaVu Sans,sans-serif;">In particular, it is proved that: 1) if a space <em>X</em> is completely regular and a space <em>Y </em>is an arcwise connected metric continuum distinct from an arc, then the pair <em>(X,Y)</em> has the graph intersection property if and only if <em>X</em> is hereditary disconnected; 2) if a connected space <em>Y</em> is fixed, then the graph intersection property holds for every pair <em>(X,Y)</em> if and only if there is a closed linear order on <em>Y</em> with minimal and maximal elements. Related results are obtained.</span></p>http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/577 |
| spellingShingle | J. J. Charatonik K. Omiljanowski Biagio Ricceri Graph intersection property Le Matematiche |
| title | Graph intersection property |
| title_full | Graph intersection property |
| title_fullStr | Graph intersection property |
| title_full_unstemmed | Graph intersection property |
| title_short | Graph intersection property |
| title_sort | graph intersection property |
| url | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/577 |
| work_keys_str_mv | AT jjcharatonik graphintersectionproperty AT komiljanowski graphintersectionproperty AT biagioricceri graphintersectionproperty |