Let (X,d) be metric space and X is unbounded, then d (z. y) . y EX, is 1+d(r,y) di de fined as dy = O metric but may be bounded or unbounded Ometricand uunbounded Ometric and bounded

Q: suppose or be the same TO X-(X,X2) And page. Y =(Y1,Y2) %3D 1/2 dz (X,y) = ( \xq-Yal"+ |x2-Y2T) max.…

A: As per company rule we will solve the first part. For other parts kindly post in other question.

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Q: Let X (2,3. 4) and de fined metrie on X as d(x, y) = |-y Find open ball B (2.2) = (0) O (2) 0 2.0…

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Q: Ik (X,d) Is a mete spate and kyo then show that di ex.y ) Kd (X)y) 1+kd (メッ) is a bounded metric on…

A: Metric Spaces Definition: Given a set X and a function d : X × X → R, we say that (X, d) is a metric…

Q: 1. Get center point of homo geneu us plane limited by 9) y =4- x2 and x axis

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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Q: Q3: (a) In the metric space (S, d), Vx,y ES. If A = where S = [0, 1]; d(x, y) = |x-yl; A = [0,2),…

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A: Simplify the integral:  ∫Ωr→r3∇→r4-R4r5+7r3+2dτ=∫Ωrr3r^r^ddrr4-R4r5+7r3+2r2sinθdrdθdϕ…

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Q: 2. Prove that if d is a metric for X, then another metric d' for X is given by if a ≤ b " if b ≤ a…

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Q: det R have the inner Euclidian fipace product 4=(5,-1) and let X= L1,1) and Find l lyll and Kxy>…

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A: Given: x=(1, 1)  and y=(5, -1)(a) ||x||=12+12             =2||y||=52+(-1)2        =25+1…

Q: 3) Find the dimension of the vectora space ganenated by the yeetons: '= (o 1 82= (2 -1 5 4) 83- (4 0…

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Q: Consider the infinite geometry R^2, where points are (x, y) ∈R and lines are ax + by + c = 0 with a,…

A: We have to show that R^2 is an Affine plane.

Q: Which among the following diagrams correspond to the metric below on the real plane R^2?…

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Q: Let de(x, y) := |x — y|, d₁(x,y) := for x,y E R. Show that (a) d₁ is a metric on R; (b) dẼ and d₁…

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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

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A: This is a problem of topology.

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Q: 0. Show that C[-1,1] c C[0,1]. C[0,1]).

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Q: 3 Let (Y, p) be a metric space. Give an example metric d on Y such that every finction f:(Y, d)→(Y,…

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