Obtainable Sizes of Topologies on Finite Sets
| dc.creator | Ragnarsson, Kari | |
| dc.creator | Tenner, Bridget Eileen | |
| dc.date | 2008-02-18 | |
| dc.date | 2009-05-20 | |
| dc.date.accessioned | 2026-07-07T13:16:13Z | |
| dc.date.available | 2026-07-07T13:16:13Z | |
| dc.description | We study the smallest possible number of points in a topological space having k open sets. Equivalently, this is the smallest possible number of elements in a poset having k order ideals. Using efficient algorithms for constructing a topology with a prescribed size, we show that this number has a logarithmic upper bound. We deduce that there exists a topology on n points having k open sets, for all k in an interval which is exponentially large in n. The construction algorithms can be modified to produce topologies where the smallest neighborhood of each point has a minimal size, and we give a range of obtainable sizes for such topologies. | |
| dc.description | Final version, to appear in Journal of Combinatorial Theory, Series A | |
| dc.identifier | https://arxiv.org/abs/0802.2550 | |
| dc.identifier | http://arxiv.org/abs/0802.2550 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230722 | |
| dc.subject | Combinatorics | |
| dc.subject | General Topology | |
| dc.subject | 06A07 (Primary); 54A99, 05A99 (Secondary) | |
| dc.title | Obtainable Sizes of Topologies on Finite Sets | |
| dc.type | text |