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\title{
Exam for Topology \\ winter semester 2023/2024
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\section*{Questions set no. 2}

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\textbf{1.} 
Give a definition of a metric space. Provide examples. What are relation(s) 
between the notions of a metric space and a topological space?


\bigskip


\textbf{2.}
Do there exist two topological spaces, and a continuous map between them, such 
that:
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a) the image of any open set is closed?
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b) the image of any closed set is open?
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c) the conditions a) and b) are satisfied simultaneously?


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