Question 4: Let X be any set. Let B1 a base of a topology T1 on...

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Question 4: Let X be any set. Let B1 a base of a topology T1 on X and B2 a base of a topology 72 on X. Prove that 71 = 2 if and only if for every a E X and any U € BỊ with a E U there exists a V e B2 such that æ € V CU, and for any V E B2 with a e V there exists a U € B1 such that a E UCV. [10] Question 5: Let X be a topological space and let A, B C X such that A = 0 = B. Show that (AUB)° = 0 [4] Question 4: Let X be any set. Let B1 a base of a topology T1 on X and B2 a base of a topology 72 on X. Prove that 71 = 2 if and only if for every a E X and any U € BỊ with a E U there exists a V e B2 such that æ € V CU, and for any V E B2 with a e V there exists a U € B1 such that a E UCV. [10] Question 5: Let X be a topological space and let A, B C X such that A = 0 = B. Show that (AUB)° = 0 [4]