Let f be a function that maps Xinto Y (f:X → Y ). Let {Gα| α ∈ A} be an indexed family of subsets of Y. Show f −1 (⋂αεA Gα) = ⋂ f −1 α∈A (Gα)

Q: Let F be the co

A: Here,for G∈F and △∈D={cG1-G2:CER,Gj∈F, j=1,2}. Then, TG+t△-TG=∫G+t△z-ydG+t△ y-∫Gx-ydGy…

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A: Let S be the set S = {a, b, c, d} and consider the function f : PS → ℤ given by f(X) = |X| Where X…

Q: #7) Show that f(-) is a convex function if and only if epi(f) C R"+¹ is a convex set. Let us denote…

A: Kindly refer to Step 2 for the solution.

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A: Given is set of all functions from set of reals to set of reals

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A: Consider

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Q: A = {2, 3, 4, 5} and B et f : A → B be a func ow. Which of the following

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Q: Let X = {o, p, s, w}, Y = {a,b, e, g, k}, and Z = {1, 2, 3, 5, 7, 9}. Let ƒ : X → Y where f = {(o,…

A: X=o,p,s,wY=a,b,e,g,kZ=1,2,3,5,7,9f:X→Yf=o,a,p,g,s,e,w,bg:Y→Zg=g,3,e,2,b,9,k,7,a,1

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A: No information is given for topology on Y So i have solved only the middle question

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Q: Metrics. Show that, for fixed x0 in E, the function  from E into ℝ+ is uniformly continuous.

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Q: et F be the collection of

A: To define, T(G)=∫G(z-y)dG(y),G∈F

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Q: f: (R, +) → (R*, .) where f(x) = 2*

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Q: Prove that if f is a constant function on [a, b] then f = S(f,P) for any tagged partition P of [a,…

A: This is a question of R integration.

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Q: Let fi : R" –→ R and f2 : R" → R be two functions. (5.1) Consider the following proposition: If…

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Q: ) Let f be a continuous function that maps a finite closed interval [a, b] into itself. Prove that f…

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A: Given: f:X→Y and a,b⊆X, Find out: To choose the correct option.

Q: Let the function ƒ : [0, 1] →R be defined by { if x = ! (n = 1, 2, 3, · · · ) f(x) = n 1– x2…

A: Given :  f : [0, 1] →ℝ  defined by ;              fx = ex2,if  x=1n    (n=1, 2, 3, ...…

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Q: prove If f:X→Y is a function and F is a non empty family of subsets of y, then o(f¹(I)) = f¯¹ (o(I))

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Q: For functions:f(x, y) = x − yg(x, y) = x2 + x − yDetermine whether the following sets are closed and…

A: Final answer:.a) Not bounded.b) Not bounded.c) Not bounded.d) Not bounded.Explanation:Explanation:…