Prove that the metric ∞ in Rn given by da(x,y)= max {1x₁-yil,xn-yol } satisfies the axioms of the metric

Q: Let L be the line in R2 through the points [:] } Find a linear functional f and a real number d such…

A: First, we will find the equation of a line given two points.

Q: Prove C(x) with the supremum norm is a metric space by showing the supremum norm is a metric

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Q: Suppose f(z) is analytic in the unit disk D={|z| < 1} and |f(z)|<= 1 for |z| <1, Prove that…

A: Assume that f(z) is analytic on the unit disk D ={z: |z| < 1}.Also assume that |f(z)|≤1 for…

Q: ) Consider the space R^2 equipped with the sunflower metric. Identify explicitly the set of points…

A: The objective of the question is to identify the set of points in R^2 that form a ball of radius 1…

Q: Any two-dimensional metric satisfies Rxpμv (grµg pv - grv 9pp). Show that the vacuum Einstein…

A: The vacuum Einstein equations are given by:Rμν−12gμνR=0 where Rμν ​ is the Ricci tensor, R is the…

Q: Prove that the Peano Curve is continuous and surjective mapping [0,1] onto the unit square

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Q: Show that the parametric curve r(t)= , t [-1,1] is smooth and compute its lengh

A: The given parametric curve is: r(t)=t1+t2, 11+t2 ;          t∈-1, 1

Q: Verify that the discrete metric is actually a metric.

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Q: Let fi(x) E Fun (R,R) be the constant function I, wheret ficx)=1 for all xG RRe Prove that S { sec?…

A: Given: fx∈funℝ, ℝ is a constant function. such that: fx=1……1 S=sec2x, tan2x, fx

Q: Theorem 9.13. Let (X, d) and (Y,e) be metric spaces. Then X × Y is a metric space.

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Q: Create a vector-valued function whose graph is an ellipse, centered at (1, 2) with horizontal major…

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Q: the metric space symmetry condition of the discrete metric, I find myself writing that if d(x,y)=0…

A: Let (X,d) be a metric space, where d is the discrete metric. Then, for any x,y∈X, we have: d(x,y) =…

Q: Show that the Euclidean metric is a metric( i.e. verify that the function d satisfies the three…

A: Here we have to show thatt Euclidean metric is a metric.

Q: Sketch each of the following sets and decide if they are open sets. Give brief reasor for your…

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