Question: This is a real analysis topic Question regarding uniform continuity and metric spaces. Is it possible for a function to be uniformly continuous on Q

This is a real analysis topic

Question regarding uniform continuity and metric spaces.

Is it possible for a function to be uniformly continuous on Q (or a subset of Q), but not uniformly continuous on R (or the corresponding subset of R)? Any examples? I think the reverse "uniformly continuous on R but not Q" is false because Q is a subset of R. But I wonder about the former statement.

Thanks!

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!

Functional analysis Questions 81 17:35 Expert Q&A W + 3. Prove that the metric space ( of all bounded scalar sequences is complete. Recall that the metric on 2 is given by doo (x, y) = sup | - Vil,...

Question 1 Consider the trigonometric series een -1 +n the series's sumfunction is defined f. The following questions should be answered (preferably) without determine the function for f. 1. a)...

Real Analysis question about uniform continuity. I know that a constant function is uniformly continuous. We have a function f: [0,+inf] - > R Say f(x) = 1 for x in [0,1] and f(x) = 2 for x in...

I am really desperate for someone to answer all 4 parts of this question (d, e, f, and g) (I have already posted this question twice and no one has answered all 4 parts sufficiently). This is due in...

nodes, but at least its bias can be quantified by Markov Chain L. INTRODUCTION analysis and thus can be corrected via appropriate re-weighting The popularity of online social networks (OSNs) in...

> " ! Help / FAQ # Alicia Clark $ > 12.1 Probability of an event One of the primary applications of counting is to calculate probabilities of random events. Probabili theory plays an important role...

Flag question: Question 1 Question 1 1 pts A client wants to reduce the property's hazard insurance coverage substantially, in order to save money on the premiums. If the property manager tries to...

JPMA-01726; No of Pages 12 Available online at www.sciencedirect.com ScienceDirect International Journal of Project Management xx (2015) xxx - xxx www.elsevier.com/locate/ijproman Does Agile work? A...

this is my assessment which are am going to send you and i need some things about my assessment : Adding some more detail and diving into the case study a bit deeper would really make your points...

I need the multiple choice questions answers from chapter 4 and 5 of the attached & Monograph...

Diana has owned an investment property for several years. In late September, the property became vacant and she decided to carry out the following work with a view to letting it at a higher rent:...

Is workplace bullying different from discrimination? Explain.

Your firm is contemplating the purchase of a new $ 5 4 5 , 0 0 0 computer bavied order entry system. The system will be deprecioted straight line to zero over ifs five - yoar ife. It will be worth $...

Exercise 13-37 (Algo) Estimate Purchases and Cash Disbursements (LO 13-3, 4) Montrose Instrumentation produces measurement equipment. One component, used in a variety of the company's products, is...