Lijović, Marija (2015) Izračunljivi topološki prostori. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract
This thesis consists of three main parts. The first part of thesis is devoted to the basic terms of computation, definition of recursive function $\mathbb{N}^k \to \mathbb{Z}, \mathbb{N}^k \to \mathbb{Q}$ and $\mathbb{N}^k \to \mathbb{R}$ as well as to some important results regarding these recursive functions. The definitions of metric and topological spaces are presented in the second part of thesis. This part states and discusses the main results related to the continuity, convergence of sequence, compactness, Hausdorff spaces as well as to the notion of a basis for a topology. The third part of thesis is dedicated to the computable topological spaces. Introduction of computable topological spaces was motivated by computable metric spaces and some of its important properties.
Item Type:  Thesis (Diploma thesis) 

Supervisor:  Iljazović, Zvonko 
Date:  2015 
Number of Pages:  65 
Subjects:  NATURAL SCIENCES > Mathematics 
Divisions:  Faculty of Science > Department of Mathematics 
Depositing User:  Iva Prah 
Date Deposited:  21 Oct 2015 09:08 
Last Modified:  21 Oct 2015 09:08 
URI:  http://digre.pmf.unizg.hr/id/eprint/4293 
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