Original title:
Aplikace Baireovy věty
Translated title:
Aplikace Baireovy věty
Authors:
Peprníková, Ľubica ; Simon, Petr (advisor) ; Pyrih, Pavel (referee) Document type: Bachelor's theses
Year:
2009
Language:
eng Abstract:
[eng][cze] The aim of this work is to show, having three di®erent spaces and a set of elements with some common property in each one of them that the given set is the set of typical elements in that space. First we will show that a typical continuous function deffined on the interval [0; 1] is a nowhere differentiable one. Then we will show that a typical compact set in R2 is a discontinuum. And lastly, we will show that a typical planar continuum is an indecomposable one. A valuable tool will be the Baire theorem, the use of which will ensure, besides the density, also the fact that the given set is a countable intersection of open sets.Cielom tejto práce je v troch roznych prípadoch dokázat', že množina prvkov s danou vlastnost'ou je množina typických prvkov. Najskor dokážeme, že typická spojitá funkcia, definovaná na intervale [0; 1], nemá deriváciu v žiadnom bode. Potom dokážeme, že typická kompaktná podmnožina R2 je diskontinuum. A napokon ukážeme, že typické rovinné kontinuum je nerozložitel'né. Doležitým nástrojom bude Baireova veta, ktorej použitie nám okrem hustosti zaistí zároveň aj to, že daná množina je spočetným prienikom otvorených množín.
Institution: Charles University Faculties (theses)
(web)
Document availability information: Available in the Charles University Digital Repository. Original record: http://hdl.handle.net/20.500.11956/31034