Homotopska razdalja
delo diplomskega seminarja
Abstract
V homotopski teoriji enačimo preslikave, ki so med seboj homotopne. Za poljubni preslikavi iz $X$ v $Y$ iščemo podprostore $X$, na katerih sta homotopni. Najmanjše število takih podprostorov, ki domeno $X$ pokrijejo, razglasimo za njuno homotopsko razdaljo. Z uporabo lastnosti homotopije in razširjanjem pokritij normalnih prostorov dokažemo, da je homotopska razdalja na njih metrika.
Homotopsko razdaljo povežemo s Lusterik-Schnirelmannovo kategorijo in topološko kompleksnostjo. Povezave med njimi nam poenostavijo dokaze njihovih lastnosti in jih predstavijo v novi luči.
Keywords
homotopija;homotopska razdalja;homotopska ekvivalenca;trikotniška neenakost;Lusternik-Schnirelmannova kategorija;kategorična množica;topološka kompleksnost;vlaknenja;prerezna kategorija;
Data
| Language: | Slovenian |
|---|---|
| Year of publishing: | 2024 |
| Typology: | 2.11 - Undergraduate Thesis |
| Organization: | UL FMF - Faculty of Mathematics and Physics |
| Publisher: | [A. Zaletelj] |
| UDC: | 515.1 |
| COBISS: |
200520195
|
| Views: | 60 |
| Downloads: | 14 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | English |
|---|---|
| Secondary title: | Homotopic distance |
| Secondary abstract: | In homotopy theory we identify maps that are homotopic. For two mappings from $X$ to $Y$ we look for subspaces of $X$ on which they are homotopic. The minimum number of such subspaces covering the domain $X$ is declared to be their homotopic distance. Using properties of homotopy and extending the covers of normal spaces, we prove that the homotopic distance on them is a metric. We connect homotopic distance with Lusternik-Schnirelmann category and topological complexity. The links between them simplify the proofs of their properties and present them in a new light. |
| Secondary keywords: | homotopy;homotopic distance;homotopy equivalence;triangular inequality;Lusternik-Schnirelmann category;categorical set;topological complexity;fibrations;sectional category; |
| 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: | 39 str. |
| ID: | 24512084 |
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