Vukić, Slavica (2015) HahnMazurkiewiczev teorem. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract
The HahnMazurkiewicz theorem is one of the most important results in the history of pointset topology, because it completely solves the problem of “spacefilling” curves. It states that a Hausdorff space is a continuous image of a line segment if and only if it is a Peano continuum, that is, compact, connected and locally connected metric space. In this B.sc. thesis we give a short description of the problem and present a proof of this theorem. The fact that a continuous image of a line segment is a Peano continuum is a simple consequence of the Urysohn metrization theorem combined with the fact that local connectedness is preserved by a continuous closed map. To prove the other direction of our theorem we use the AleksandroffHausdorff theorem about the existence of continuous mapping of the Cantor set onto an arbitrary compact metric space and we continuously extend this mapping over the line segment.
Item Type:  Thesis (Diploma thesis) 

Supervisor:  Iljazović, Zvonko 
Date:  2015 
Number of Pages:  35 
Subjects:  NATURAL SCIENCES > Mathematics 
Divisions:  Faculty of Science > Department of Mathematics 
Depositing User:  Iva Prah 
Date Deposited:  29 Oct 2015 12:26 
Last Modified:  29 Oct 2015 12:26 
URI:  http://digre.pmf.unizg.hr/id/eprint/4198 
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