Let f: X Y be a continuous surjection between metric spaces. If X is compact then .............................   A. X is complete   B. Y is connected.   C. Y is not compact.   D. Y is not neccessarily complete.

Q: Let M = {0,1} and d be the discrete metric, then d is not complete %3D O True O False

A: Discrete metric space.

Q: A and Bare open and bounded.

A: For second one we can take any two open interval one of whose right end point ar same of the others…

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Which sets are open in the metric space (IR, d), v i). [1, 2) ii). (1, 2) U (2, 3)

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A:

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A: I have proved all three conditions gor norm

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Q: Let X = R. and d is discrete metric, Find S (2,2) OR O (2) O {0} (2)

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Q: The set X is an open set in the ambient metric space . True O False Reset Selection Rationale:

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A: A set E is closed in X if it contains all of its limit points.

Q: Q2: In usual topological space (R.T), answer the following: 4- Is [0,1] is arcwise in R? Why?

A: Given that ℝ, Tu is usual topological space. To show: 0,1 is arcwise in ℝ.

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnC = ¢, BnC = ¢, µ(An B) = 0. Determine µ(AUBUC).

A: Measure theory

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Q: Let (X, B(R), ft) be a Borel measure space. ANC= 6 BOC =0 p(AnB) = 0. Determine ju(AUBUC) %3D

A: Since sets are disjoint so measure will be the sum

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Q: Proposition 2.18. Let (X,T) be a topological space : (1) (A°)° = A°. (2) ACB⇒ A° C B° for all A, B €…

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnC = 4, BnC = ¢, µ(An B) = 0. Determine µ(A UBUC).…

A: Measure

Q: A(n)............ is the collection of all points in the plane the sum of whose distances from two…

A: It is given that,   A(n) ............ is the collection of all points in the plane the sum of…

Q: QUESTION 15 Let f. X Y be a continuous surjection between metric spaces. If X is compact then O AX…

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A: Given f: X →Y be a continuous surjection between metric spaces.

Q: ! 0. JUUTTUU M 10. Compute the distance between the functions f(x) = 5 + x and g(x) = 6 + 3x in…

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Q: d(r, y) Let (X, d) be a metric space and let p(r, y) = for all r, y E X. Show that (X, d) 1+d(x, y)…

A: According to our company policy we are supposed to answer only first question i.e. (4) 4) in this…

Q: Define on R, the metric d defined by d(x, y) = |1+1리 1+ |y| Then (R, d) is not complete. True False

A: Given

Q: Let A be a non-empty subset of the metric space (X,d). show that a. d(x, A) – d(y, A)| < d(x, y)For…

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Q: 1- Suppose that ,p) is a meric space, an that E CX. Then the interior E is open (m X) and the…

A: The given question is related to metric spaces. The solution is explained below.