Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. let (x, dx) and (y, dy) be metric spaces.define th

Let (X, dX) and (Y, dY) be metric spaces.Define the function d : (X × Y )...

70.2K

Verified Solution

Question

Advance Math

Let (X, dX) and (Y, dY) be metricspaces.Define the function

d : (X × Y ) × (X × Y ) ? R

by

d ((x1, y1),(x2,y2)) =dx(x1,x2)+dy(y1,y2)

Prove that d is a metric on X × Y .

Answer & Explanation Solved by verified expert
3.9 Ratings (648 Votes)
    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

A.) The equilibrium constant for the reaction A(g) ⇌ B(g) is 102 . A reaction mixture...

Chemistry
Q

The mechanism of DNA repair describe in details (more than 1500 words)

Biology
Q

Explain how you see the relationship between the three elementary row operations performed on an augmented...

Advance Math
Q

What occurred as a result of the protest outside the Democratic National Convention in Chicago...

Biology
Q

The displacement of a particle in simple harmonic motion in one time period is 1...

Physics
Q

To three decimal places, the slope of the tangent to the curve f(x) = log??x,...

Basic Math
Q

3 points Find a larger integral that converges or a smaller integral that diverges 5...

Calculus
Q

Tutorial Exercise Find the limit Use l Hospital s Rule where appropriate If there is...

Calculus
Q

1 Use the definition of the derivative to show y f x x is f...

Calculus
Q

Vials in a chemistry lab are marked with letters Each vial is filled with a...

Algebra
Q

Question 3. The following balances were taken from Malabar Company as at 31.12.2018 Name of...

Accounting
Q

The following is a list of independent scenarios. Assume that each corporation adopts ASPE. a....

Accounting