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Question: acu bcv and unv0 l dcus u anu v such...

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ACU, BCV, and UnV=0. l DCUS U anu V such that 5. Do this problem after we study the product topology. Let X be an infinite set. Consider (X, CF) and ([0, 1], T), X with the cofinite topology and 10,1) with the indiscrete topology. Prove that the product space X × {0,1} does not satisfy any separation axiom. Hint: First prove that X × {0,1} is not TO, then prove that no two nonempty open subsets of X x [0, 13 are disjoint. Now, find two closed nonempty disjoint subsets and complete the details.

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