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\title{
Exam for Topology \\ winter semester 2025/2026
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\section*{Questions set no. 9}

\bigskip

\textbf{1.} 
Give defintion of a connected component of a topological space, and of
conneced topological spaces. Provide examples.

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\textbf{2.}
Do there exist two topological spaces $X$ and $Y$ with the following property:
for any map $f: X \to Y$, $f$ is continuous if and only if $f$ is open?

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