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\title{
Exam for Topology \\ winter semester 2025/2026
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\section*{Questions set no. 5}

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\textbf{1.} 
Give a definition of a base of topological space. Provide examples.
Formulate and proof a criterion for a set to form a base.


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\textbf{2.}
Is it true that:

a) the product of two discrete topologies is discrete;

b) the product of two trivial topologies is trivial?


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