Eksponenti topoloških prostorov

delo diplomskega seminarja

Petra Ivana Reberc (Author), Andrej Bauer (Mentor), Davorin Lešnik (Co-mentor)

Abstract

Zanima nas, kdaj lahko na prostoru zveznih funkcij $C(X, Y)$ vpeljemo eksponentno topologijo. Ugotovimo, da je to odvisno predvsem od lastnosti prostora $X$ oziroma domene, in z obravnavanjem prostora Sierpińskega kot kodomeno poenostavimo problem. Raziskujemo topologije na družinah odprtih množic in se tako približujemo iskanemu pogoju. Ugotovimo, da mora biti $X$ sržno kompakten in podamo eksponentno topologijo za dani $X$.

Keywords

matematika;eksponentna topologija;eskponenciabilnost;sržno kompaktni prostori;šibka topologija;krepka topologija;Scottova topologija;topologija Aleksandrova;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[P. I. Reberc]
UDC:	515.1
COBISS:	18441305
Views:	557
Downloads:	234
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Exponentiable spaces and the exponential topology
Secondary abstract:	We would like to know when is it possible to endow $C(X, Y)$ with an exponential topology. We observe this depends mainly on the properties of the domain $X$ and then we simplify the problem by considering the Sierpiński space as the codomain. We explore topologies on topologies and approach the desired criteria. We find out $X$ has to be core compact and find the adequate exponential topology.
Secondary keywords:	mathematics;exponential topology;exponentiability;core-compact spaces;weak topology;strong topology;Scott topology;Alexandroff topology;
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:	28 str.
ID:	10960819