# Kvocijentni prostori

Švenda, Lovro (2015) Kvocijentni prostori. Diploma thesis, Faculty of Science > Department of Mathematics.

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Language: Croatian

This paper investigates the properties of topological spaces where the topology is induced by a quotient map. Sufficient conditions on spaces $X$ and $Y$ and a map $f : X \to Y$ so that the induced map $\bar{f}$ is a homeomorphism are found. (Corollary 2.3.21). The example with a circle shows that quotient topology $\mathcal{F}$ indicates the choice of the points to be identified or "glued" together. Other examples (Möbius strip, torus and Klein bottle) are constructed directly, by giving the quotient topology.