Let A(0, π) υ (π, e 1| Find the limit point(s) of A. а. b. Is A an open set?

Q: Show that d given by d(x, y) = |x-ylis a metric on R by using definition 4.2.1. You may want to use…

A: we knew  that given metric d(x,y) = |x-y| is always ≥0.  now d(x,y) = 0 ⇔ |x-y| = 0…

Q: Consider sets A and B with |A| = 7 and |B| = 4. How many functions f: A → B are surjective?

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Q: 2. Is the set D = | = {z = C | |z| = 5, |z − i| > 5} compact (C is equipped with a standard metric)?

A: We are given a set defined as . We want to determine if this set is compact in the complex plane…

Q: Let A = {a{a}}, B = {0.b}. C = {{0}.c.{0.c}} and D = {0}. Find following cardinalities: a) |4|= |B\=…

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Q: . Sketch the graph of the set defined by A x B where A is the closed interval [-2, 4] and B = {1, 3,…

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Q: 3. Use the definition of convex sets to answer the following: Show that if the sets S and T are…

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Q: Set X is convex if

A: Given that a set X is convex if  . . . .

Q: 3. Let f: A→ Band g: B → Cdenote two functions. Show that if gofis 1-1, then fis 1-1. D JCI

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Q: explicit

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Q: Let x be an interior point of a subset S of a metric space (X,d). Show that x must also be a limit…

A: Interior Point: Let A be a subset of metric space X, d. A point x∈A is called an interior point of A…

Q: A and B be two sets, each one of them having a minimum. Assume that A n B is not ty. Then An B has a…

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Q: 2. Classify each of the following sets as open, closed, neither, or both. Then, find the closure. a)…

A: classify the given sets are open and closed.

Q: Let Si = { x ∈ R ∣ x > i } , i=0,1,2,... Are the sets S1, S2, S3 . . .  are mutually disjoint?

A: If two sets A and B are mutually disjoint, then A∩B=ϕ . Define the sets S1 , S2 , S3 as follows.…