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Is this true?

An arbitrary intersection of open sets is open

No — it is false.

The counterexample

∩, 1/n) = {0}

Only finite intersections preserve openness.

The kind of mistake this is

Finite-dimensional intuition

Something true in ℝⁿ, or in a nice space, assumed in general.

Drill statements like this
topologyreal analysis

Others that fail the same way

From Metric Spaces › Open/closed sets, limit points, closure, interior

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