Končni topološki prostori
delo diplomskega seminarja
Abstract
Topologije na končnih množicah so pogosto po krivici spregledane, bržkone zato, ker je vsaka Hausdorffova topologija na končni množici avtomatično diskretna. Ko pa začnemo obravnavati tudi topologije, ki niso Hausdorffove, se nam odpre povsem nov svet. Izkaže se namreč, da lahko s pomočjo končnih topologij modeliramo šibki homotopski tip poljubnega končnega poliedra. V diplomskem delu predstavimo homotopsko in šibko homotopsko klasifikacijo končnih topoloških prostorov.
Keywords
končni topološki prostori;šibka homotopska ekvivalenca;homotopska ekvivalenca;delno urejena množica;simplicialni kompleks;
Data
| Language: | Slovenian |
|---|---|
| Year of publishing: | 2024 |
| Typology: | 2.11 - Undergraduate Thesis |
| Organization: | UL FMF - Faculty of Mathematics and Physics |
| Publisher: | [C. Ravnikar] |
| UDC: | 515.1 |
| COBISS: |
200239107
|
| Views: | 73 |
| Downloads: | 10 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | English |
|---|---|
| Secondary title: | Finite topological spaces |
| Secondary abstract: | Oftentimes, topologies on finite sets are unjustly overlooked, most likely because a Hausdorff topology on a finite set is automatically discrete. However, if one also chooses to consider non-Hausdorff topologies, a whole new world opens up. As it turns out, finite topologies can be used to model weak homotopy type of any finite polyhedron. In this thesis we present a homotopy and a weak-homotopy classification of finite topological spaces. |
| Secondary keywords: | finite topological spaces;weak homotopy equivalence;homotopy equivalence;partialy ordered set;simplicial complex; |
| Type (COBISS): | Final seminar paper |
| Study programme: | 0 |
| Thesis comment: | Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja |
| Pages: | 52 str. |
| ID: | 24505506 |
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