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National Repository of Grey Literature 2 records found  Search took 0.02 seconds. 
Rectagles inscribed in Jordan curves.
 Ye, Tomáš ; Šír, Zbyněk (advisor) ; Vršek, Jan (referee)
We will introduce quotients, which are very special kinds of continuous maps. We are going to study their nice universal properties and use them to for- malize the notion of topological gluing. This concept will allow us to define interesting topological structures and analyze them. Finally, the developed theory will be used for writing down a precise proof of the existence of an inscribed rectangle in any Jordan curve. 1
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Jordan Curve Theorem
 Dudák, Jan ; Vejnar, Benjamin (advisor) ; Kurka, Ondřej (referee)
Title: The Jordan Curve Theorem Author: Jan Dudák Department: Department of Mathematical Analysis Supervisor: Mgr. Benjamin Vejnar, Ph.D., Department of Mathematical Analysis Abstract: The crucial part of this work is the proof of the Jordan curve theorem. To this end, the work starts by introducing necessary notions (e.g. a curve or an arc) and showing their basic properties. Further on, the Brouwer fixed point theorem is proved (in the 2-dimensional case) as well as some of its corollaries which are then used (together with several other proven assertions) in the proof of the Jordan curve theorem. The last chapter of this work briefly informs about possible generalisations of the Jordan curve theorem, referencing to appropriate bibliography. Keywords: Jordan curve, arc, plane, connected component 1
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