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Title:
Hahn-Mazurkiewiczev izrek
Authors:
ID
Erhatič, Karmen
(
Author
)
ID
Banič, Iztok
(
Mentor
)
More about this mentor...
Files:
UN_Erhatic_Karmen_2016.pdf
(721,57 KB)
MD5: 4A324A28C2386BFDDB54A4258BF17060
Language:
Slovenian
Work type:
Undergraduate thesis
Typology:
2.11 - Undergraduate Thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
Diplomsko delo obravnava Peanove kontinuume in njihove lastnosti, ter Hahn-Mazurkiewiczev izrek. V prvem delu bomo definirali pojme in dokazali izreke, ki so bistvenega pomena za razumevanje Hahn-Mazurkiewiczevega izreka. Pri tem bo poseben poudarek na lokalni povezanosti prostora in primerih le teh. Osrednji del se bo začel z definicijo Peanovega prostora in lastnosti S. Zaključili bomo z Hahn-Mazurkiewiczevim izrekom in bomo s tem dokazali, da je vsak lokalno povezani kontinuum zvezna slika intervala [0,1].
Keywords:
lokalna povezanost
,
šibke verige
,
lastnost S
Place of publishing:
Maribor
Publisher:
[K. Erhatič]
Year of publishing:
2016
PID:
20.500.12556/DKUM-62612
UDC:
515.127(043.2)
COBISS.SI-ID:
22583816
NUK URN:
URN:SI:UM:DK:U4HKHGUA
Publication date in DKUM:
27.09.2016
Views:
1155
Downloads:
103
Metadata:
Categories:
FNM
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Secondary language
Language:
English
Title:
The Hahn-Mazurkiewicz theorem
Abstract:
In this graduation thesis we will be looking at Peano continua, their caracteristics and the Hahn-Mazurkiewich theorem. The first chapter will contain definitions and theorems that are crucial to understanding the Hahn-Mazurkiewicz theorem. There will be a special weight on local connectivity of spaces and examples of these. The central part will begin with the definition of Peano space and property S. We will end with proof of the Hahn-Mazurkiewicz theorem and thus prove that each locally connected continuum is a continuus image of the closed interval [0,1].
Keywords:
local conectivity
,
weak chain
,
property S
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