Question: Prove the following definition. From a complex open set C ( [ 0 , 1 ] ) we have the distance function: d ( g

Prove the following definition. From a complex open setC([0,1])

we have the distance function:d(g,k)=maxx[0,1]g(x)k(x)

Here, show the triangle inequality of the distance function above.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Audit the segment on Sarbanes-Oxley (26-1a) and the informant prerequisites in the Securities Exchange Act of 1934. 1. Under Sarbanes-Oxley, list the three occasions that a reviewer would have to...

Q:

Audit the segment on Sarbanes-Oxley (26-1a) and the informant prerequisites in the Securities Exchange Act of 1934. 1. Under Sarbanes-Oxley, list the three occasions that a reviewer would have to...

Q:

MATH 4011 Final Exam Review 1. Use induction to prove the following form of Bernoulli's inequality: If x > -1 then (1+x)" 21+nx VneN. 2. Use the field and order axioms for R to prove the following:...

Q:

. Answer the following questions. 1. (3 points) In Metropolis only taxicabs and privately owned automobiles are allowed to use the highway betwem the airport and downtown. The market for taxi cab...

Q:

Possible Multiple Choice Questions for the Exam. Focus on the topics discussed in class. Chapter 1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____...

Q:

.QUESTION .all the questions to be thoroughly explained Invocations of its type operations involve no writes to persistent memory and no output to clients. Concurrent processes may invoke the object....

Q:

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Q:

M361K - Intro to Real Analysis Coverage: Second half of Chapter 4 (Exercise 4.4 onward), Chapter 5, Chapter 6 Definitions/concepts to Know: D.1: Convergence (of sequences): Define what it means to...

Q:

Consider a firm with the technology yt = f (kt) where f : R+ ! R is continuously differentiable and strictly increasing. Capital is the only input in this rm and the initial capital stock k0 is...

Q:

Random Walks Using JAVA In this lab you will develop a class that models a random walk and write two client programs that use the class. A random walk is basically a sequence of steps in some...

Q:

A metallic block (specific heat 500 J/kg K) of 100 kg mass having a temperature of 360 K is immersed in an insulated tank containing 40 kg of water at 300 K. Find the change in entropy of the...

Q:

A review of Pueblo Company's balance sheet revealed a beginning balance in its Land account of $150,000. The ending balance In the account was $225,000. Ail transactions associated with the purchase...

Q:

Consider the following cash flows: YearCash Flow 0 $ 6 , 8 0 0 1 1 , 9 5 0 2 4 , 1 0 0 3 1 , 7 5 0 4 1 , 4 5 0 What is the payback period for the cash flows? Note: Do not round intermediate...

Q:

i just need d)estimate outputs with calculation of table and diagram and e)result estimated The COLOURFUL Textile Atelier was controlled by INSPECT and found to be in violation of several safety...

Q:

2. To understand that as a general rule it takes about 3 minutes before the other part(s) have made up a 90% impression of you.

Q:

3. To understand that the first impression means a lot, and it takes a lot of energy to change this first impression.

Q:

Go, do not wait until I come