Let X be a metric space. Let A and B be separated sets in X. Show either E is a subset of A or E is a subset of B where E is a connected subset of A U B.

Q: Let X be any set with the discrete topology. Show that X is normal.

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Q: • A is open in X. • A = Int A • A contains none of its boundary points. • Every point of A has a…

A: As per the company rule, we are supposed to solve one problem. Therefore kindly repost the remaining…

Q: Let

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Q: B. Given a metric space M with metric d, verify that any ε-ball is an open set. (Please If possible…

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Q: 10. a b C d a + 3b = c b+c+a=d

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Q: Let A and B be open sets in a topological space. Is A ∩ B open?

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Q: Say whether (?, ?) is a topological space. Briefly explain your answer i. ? = R, and ? =…

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Q: Let ?1and ?2 be compact subsets of a metric space X. Show ?1 ∪ ?2 is compact

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Q: Exercise 1. Let X be a metric space. The subsets of X which are arbitrary (finite or infinite)…

A: What is Open Set: Open sets in a metric space are those that, for every point P, include all other…

Q: A, B be subsets of a metric space. Show that A U B = B and that A B. Give an example to show that An…

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Q: Given a metric space M with metric d, verify that any e-ball is an open set.

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Q: Let H = Span{1+x,1+x², 3+x +2x², 2 + x + x²}. what is dimH?

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Q: Prove that if X,d is a metric space and G ⊆ H ⊆ X, then G-bar ⊆ H-bar.

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