A note on systems of rectangular islands the continuous case /
A real-valued height function / is defined on a closed rectangle R. A rectangle S C R is an /-island if there exists an open set G C R containing S such that f{x) < infs f for every x 6 G\S. The set of all /-islands is called a system of (rectangular) islands. In this paper we prove that there ex...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
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Bolyai Institute, University of Szeged
Szeged
2011
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| Sorozat: | Acta scientiarum mathematicarum
77 No. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16376 |
| Tartalmi kivonat: | A real-valued height function / is defined on a closed rectangle R. A rectangle S C R is an /-island if there exists an open set G C R containing S such that f{x) < infs f for every x 6 G\S. The set of all /-islands is called a system of (rectangular) islands. In this paper we prove that there exists a maximal system of islands of cardinality No> and that the size of a maximal system of islands is either countable or continuum. |
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| Terjedelem/Fizikai jellemzők: | 27-34 |
| ISSN: | 0001-6969 |