# Izračunljivi topološki prostori

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

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Language: Croatian

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.