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Question: 1 the set b 411213 is the basis for a...

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1. The set B= {{4),(1),(1,2),(13)} is the basis for a topology of X = {1,2,3,4). Determine the highest separation axiom the topology of X with basis B satisfies. 2. Prove that a metric space is normal. 3. Let F and G be path-connected subsets of a topological space X. Prove that if FnG then FUG is path-connected.

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