metric on X; let Xa denote the set X with the topology induced by d and with the topology induced by p; let f: Xa → Xp be defined by f(x) = x; Ey induced by d and To be the topology induced by p. Show that, if f is ≤ Ja.

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A: Answer C

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A: Definition: Let X and Y are topological spaces and f : X→Y be a function. We say that the function f…

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Q: 2. Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. a)…

A: The solution of given problem is given as follows :

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A: This is a problem of topology.

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Q: 1. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let P = P(A) be the power set of A. Let R be the relation on…

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Q: (2 points) Prove Prove that for all f: X Y and A, B C X, if f is one-to-one, then 4. f(A)n f(B) ≤…

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Q: The Power Set a) Let A = {a, b, c}. Find P(A). b) Let B = {0, 1} Let f: P(A) → B. The input of f is…

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Q: Let f : X → Y be a function. Define a relation R in X given byR = {(a, b): f(a) = f(b)}. Examine…

A: Given:

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