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Equip X = [0, 1]^N with the box topology. Prove or disprove the following: (a) [0, 1]^N is connected. (b) [0, 1]^N is compact.

Equip X = [0, 1]^N with the box topology. Prove or disprove the following:

(a) [0, 1]^N is connected.


(b) [0, 1]^N is compact.

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