diplomsko delo
Nataša Vasle (Author), Uroš Milutinović (Mentor)

Abstract

Moorov izrek o triodah pravi, da v ravnini obstaja le števno mnogo disjunktnih enostavnih triod. Enostavna trioda je prostor, homeomorfen črki T. Najprej bomo ponovili nekaj osnovnih definicij in izrekov iz področja topologije, nato bomo dokazali izrek o enostavnih triodah. Sledilo bo glavno poglavje, v katerem bomo preverili veliko trditev in dokazali Moorov izrek. V naslednjem poglavju se bomo ukvarjali z različnimi posplošitvami Moorovega izreka o triodah, v zadnjem poglavju sledijo primeri konkretne uporabe tega izreka pri dokazovanju obnašanja različnih funkcij na robu definicijskega območja.

Keywords

matematika;Moorov izrek;triode;kontinuum;posplošene triode;krivulje;lok;kondenzacija;domena;diplomska dela;

Data

Language: Slovenian
Year of publishing:
Source: Maribor
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [N. Vasle]
UDC: 51(043.2)
COBISS: 16876040 Link will open in a new window
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Other data

Secondary language: English
Secondary title: MOORE'S TRIOD THEOREM
Secondary abstract: Moore's triod theorem says, that there exists only a countable number of mutually exclusive simple triods in the plane. Simple triod is a space, that is homeomorfic to letter T. At first we will repeat some of the basic facts of topology, than we will prove the theorem of simple triods. Then it follows the basic chapter in which we will confirm many statements and prove Moore's triod theorem. In the next chapter we will be occupied with diferent generalisations of Moore's triod theorem, in the last chapter there will follow examples of concrete use of Moore's triod theorem to prove the boundary behavior of some maps.
Secondary keywords: Continuum;simple triod;triod;generalized triod;simple closed curve;arc;condensation point;domain;segment.;
URN: URN:SI:UM:
Type (COBISS): Undergraduate thesis
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: VI, 47 f.
Keywords (UDC): mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID: 17782
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