Answered: Use the Completion Theorem below to…

Use the Completion Theorem below to show that the Completion of the discrete metric space X is itself. S0, x = y \ 1, x # y S d(x, y) : %3D

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.7: Applied Problems

Problem 58E

See similar textbooks

Related questions

Q: Let M = {0,1} and d be the discrete metric, then d is not complete %3D O True O False

A: Discrete metric space.

Q: Let d: R? x R² →R, defined as d (x, y) = |x1 - yı|+ |#2 – y2]| where x = (x1, x2), y = (y1, y2) ,…

Q: Let m EN, m > 2 be a fixed, and consider the set Rn with a metric function d,m defined by the…

Q: Let X be an infinite set and let d be the discrete metric on X: {: 0if p=q 1 if p + q. d(p, q) = (a)…

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: Let (R. d) be discrete metric space, then Ris separ able O True O False

Q: Use the Trapezoidal Rule to estimate the number of square meters of land in a lot, where x and y are…

A: The given data is: ,,

Q: Consider R2 equipped with the Euclidean metric d2. Let A be a non-empty subset of R2 , that is…

A: Consider R2 equipped with the Euclidean metric d2. Let A be a non-empty subset of R2 , that is…

Q: non-empty set and d:X x X R de fined by d(x,y)=31 x- 41_ 2+|xl+lyl or disprove that d is a metric on…

Q: Define p: R^2 x R^2 to [0, infinity) by the rule p(x1,y1),(x2,y2)=squareroot((x1-x2)^2+(y1-y2)^2)…

Q: 3. Let Ac R' where A = {x: x 1}. Describe the quotient space topology on R'/A obtained by…

Q: The half-space consisting of the points on and below the xy-plane

A: Concept:

Q: Q2: In usual topological space (R.T), answer the following: 4- Is [0,1] is arcwise in R? Why?

A: Given that ℝ, Tu is usual topological space. To show: 0,1 is arcwise in ℝ.

Q: garded as a subset of R. 9.E. y ing theargme ang ), prove that the interval J = { (x, y) : 0 < x <…

A: 9.F We have given J=(x,y):0≤x≤1,0≤y≤1 to prove the compact in R2 we have to show that J is closed…

Q: 3. Let d(x, y) := |2 - 2| for x, y E R. . is a metric on R. Show that (R, d) is not a complete…

A: Cauchy sequence: A sequence x1, x2, x3, ... in a metric space (X, d) is called Cauchy if for every…

Q: Set (Q, M, µ) a space of o-finite measure. we define the aplication 4: L° (Q) → L'(Q)* given by =…

A: Let g,h∈L∞(Ω and α∈F Claim:- ϕ(αg+h)=αφ(g)+φ(h)

Q: (b) Let (M, d) be a metric space. Define a function e: MXM-R by e(x, y) = min {1,d(x, y)}; vx,y E M.…

Q: Let d: Rx R*→[0, ∞) such that d(XF)=√(x, y)² show that (R.d) metric space.

A: `

Q: (b) Show that x. y < ||x|| ||y||- [Hint: If x, y # 0, let a = , 6= and use the fact that ||ax + by |…

A: Given that, Euclidean metric d on Rn is defined as d(x,y) = || x - y || for x, y in Rn Part(a): Let…

Q: Sketch the space curve r(t) = −ti + 4tj + 3tk and find its length over the given interval [0, 1] .

A: Given space curve is rt=-ti+4tj+3tk. Sketch the above space curve as shown below.

Q: Let r, y E R". Show that for any sequence {r4}, {Yk} such that x → r and yk → y, we have limg-→0…

Q: Provide inequalities for r and that precisely describe the region in the xy-plane bounded by the…

Q: b) Let X = R equipped with the standard metric. Then The boundary of [a, b),(a,b),[a,b), and(a, b)…

A: This is a problem of topology.

Q: 1. Let, y eR. Determine if the following are metrics on R or not (a) d, (x, y) = /1x - y| (b)…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Consider the sets N = R? \ {(0, y) E R² | |y| > 0}, L = {(x, y) E R² | |x| = |y|}, and let dr,…

Q: 2. Let (X, d) be a metric space and y E X. (i) Prove that the closed ball B[y,2] is a closed set in…

Q: Let X=R2 and defined d2: R2 x R2 to R by d2((x1, y1)) = max{|x1-x2|, |y1-y2|} Verify that d2 is a…

A: Given a function d2: R2×R2 → R, defined by d2x1,y1,x2,y2=maxx1-x2,y1-y2. To verify that d2 is a…

Q: i) Pe(x) = 0 iff r € Ë. ii) Prove that pe is uniformly continuous.

A: i Let E is the non-empty subset of a metric space X,d the distance from x to E is defined as…

Q: Is the set S = [0,1] with the discrete metric d separable? Explain

A: We Know that a set is separable in metric space only if it contains a countable dense subset in it.…

Q: F. dr = 0 for every closed curve Cin R, an open connected region. %3D True O False

A: Explanation of the solution is given below.....

Q: 5. Let X = R? and define d, : R? ×R² →R by d (x,,y,),(x,,y2)) = max {x, – x,|-\y, -y}} . 13 a)…

Q: Exercise.3 Show that the following the functions d and p on X = R? are metrics or not, such that 2.…

Q: Let (S, d) be a metric space and suppose that ρ:S×S→R is defined by ρ(x, y) =d(x, y)/(1 +d(x, y))…

Q: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.

A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9

Q: /Evaluate The are bounded by The Semiellipes y=25-x' oP The lines X = ±1,Y=-1

Q: Consider the following space curve r (t) = t²i + 2tj – v2 43/2 k %3D 3

A: The given space curve isrt=t2i^+2tj^-423t32k^.To find:The time period when rt intersects xt+zt=0 and…

Q: Let W = Span{u} where u -2. Let y = |1, find the distance from y to W L3]

Q: Let R have its usual topology and let X = {a, b, c}. Define f : R → X by x 0 а, f(x) = с, Is X with…

Q: Verify that (S, d) is a metric space. 10.2 Prove that d(x, y) < d'(x, y)s/2 d(x, y) for all points'…

A: To prove dx,y≤d'x,y≤2dx,y for all points x,y∈ℝ×ℝ where d is the usual metric and d' is the…

Q: (c) Given the set T := {(x, y) = R²: |xy| ≤ 1}. Is T a compact set? Show your working. If you say it…

A: Given c) T=x,y∈R2:xy≤1d) Given a metric space X,ρ and two compact subsets S,T∈X

Q: (a) Consider the metric space 0 (i) if r 1.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: close ball is an open

A: Consider the metric space X,d, where d is the usual metric on ℝ4. Bra is the closed ball with centre…

Q: Let X = R², x, y EX where x = (x₁, x2), y = (y₁.Y2) with the metric function (4 pts) (x, y) =…

A: This is a question of topology and metric space.

Q: Let X=ℝ2 and define d2,:ℝ2×ℝ2→ℝ by d2((x1 ,y1),(x2,y2)) = max{|x1 - x2|,|y1 - y2|}. a) Verify that…

A: Given that X=ℝ2 and defined by d2:ℝ2×ℝ2→ℝ Part(a): Now from given d2:ℝ2×ℝ2→ℝ by…

Q: Let (S) be a metric space and suppose that p :S x S-R is defined by d(r, y) 1+ d(x, y) pla, y) = for…

Q: Let f: (N,d) (N, d), where d is the usual metric and di is the discrete metric, defined f as f (x)…

Question

Use the Completion Theorem below to show
that the Completion of the discrete metric
space X is itself.
S0, x = y \
1, x # y S
d(x, y) :
%3D

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Relations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Let X=ℝ2 and define d2,:ℝ2×ℝ2→ℝ by d2((x1 ,y1),(x2,y2)) = max{|x1 - x2|,|y1 - y2|}. a) Verify that d2 is a metric on ℝ2. b.) Draw the neighborhood N((0; 1) for d2, where 0 is the origin in ℝ2.
Define p: R^2 x R^2 to [0, infinity) by the rule p(x1,y1),(x2,y2)=squareroot((x1-x2)^2+(y1-y2)^2) Show that p is a metric on R^2.
Let X=R2 and defined d2: R2 x R2 to R by d2((x1, y1)) = max{|x1-x2|, |y1-y2|} Verify that d2 is a metric on R2
Let (R>0, d) be the metric space defined by d(x, y) =|log (y/x)|. This metric space is isometric to the Euclidean line E1, where an isometry E1 → (R>0, d) is given by x→ ex . proof that x→ ex is isometric.
use the boundary conditions to show that C=−λR.
Do the following task.a) State formally what do mean by being an open set of E inmetric space (X, d). b) Show that Q is not open in (R, d) where d(x, y) = |x − y|.
Find the maximum value of f(x,y) = x5y8 for x,y > 0 on the unit circle.
If (X, d_{1}) and (Y, d_{2}) are metric spaces, we define d: (X × Y ) × (X × Y ) \rightarrow R by d((x_{1}, y_{ 1}),(x_{2}, y_{2})) = d_{1}(x, x′) + d_{2}(y, y′).Answer the following literals a) Prove that d is a metric b) If X = Y = R with d1 equal to the usual metric and d2 the discrete metric. Describe what the balls are like with the metric d on R^{2}
consider the metric space < X, d > for the case in which the metric d is the usual metric on R'. Given the closed ball B,(a) C X with centre a = P(3, 1, 1, 1) that is located on its boundary OB. (2,0, 2, 2) and the point (i) Show that every point x 4 Br(a) is the centre of an open ball B:(x) with some feasible radius e > 0, and give the feasible range for ɛ. (ii) Use this to prove that the complement B„(a)° of the close ball is an open set.
17. Show that the function d is a metric whered(x, y) = |x − y| / (1 + |x + y|)
Consider the right triangle withvertices (0, 0), (0, b), and (a, 0), where a > 0 and b > 0. Showthat the average vertical distance from points on the x-axis to thehypotenuse is b/2, for all a > 0.
Can you prove in detail the metric space symmetry condition of the discrete metric, I find myself writing that if d(x,y)=0 and x=y then y=x which means that d(y,x)=0. But I have to prove it in a detailed manner with explanation apparently. Thank you in advance.