Why do we need finite intersection of open sets for topology?

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In this video, we are going to discuss the definition of topology. In particular, why do we need finite intersection of open sets for topology?
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00:00 - Intro
01:25 - Statement
02:45 - Example

Maksym Zubkov

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Please watch: "Real Projective Space, n=1"
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Finite intersection? More like "Fantastic information!" Thanks again for putting all these videos together.

PunmasterSTP
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But why do we need this property at all?

هيلة-عم