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}

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}

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Find the volume enclosed by the surface z = xy and over the triangle located in the plane z=0 with vertices (1, 1), (4, 1), (1, 3). (show with graph)
by Using spherical Co-ordinate find voulme of solid bounded
How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Thanks for you help. :)
A triangle is bounded by the lines y = x, y = -x, and y = 1 When setting up an intergral to find mass or inertia or whatever, why can I not set it up as integral(1, -1) integral(1, x) dydx and instead need to set it up as integral(1, 0) integral(y, -y) dxdy
Can you explain how we get for the red lines: x = a-z , z = a-y , z = 4-x-y, y = a -x and show what is the plane a-x-y-z = 0 since I do not understand it, and how I find the limits of integration
The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are attached to the ends of a light inextensible string. The string is taut and passes over a small smooth pulley fixed at the intersection of a horizontal surface and an inclined plane.The block can move on the horizontal surface, which is rough. The particle can move on the inclined plane, which is smooth and which makes an angle of θ with the horizontal where tanθ = 3/4The system is released from rest. In the first 0.4 seconds of the motion P moves 0.3m downthe plane and B does not reach the pulley.(a) Find the tension in the string during the first 0.4 seconds of the motion.(b) Calculate the coefficient of friction between B and the horizontal surface.
Find the volume of the solid bounded by z = 9 - y2 and plane x = 2 on the first octant.
A region R consists of a square bounded by the lines x = −7, x = 7, y = 0, and y = −14and a half disk bounded by the semicircle y = (49-x^2)^(1/2) and the line y = 0.Find the center of gravity, (x, y), of R.
Find the volume of the solid in the first octant bounded bythe cylinder z=16 -x2 and the plane y=5
Discuss the hyperbolic geometry of spacetime in comparison to circular geometry of 3-vector space.
Find volume y=3x^2, x=1, and y=0 about x axis
Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant