Question: (9) (a) Let 6 > 0 and let E (2 [a,b] be a set of points satisfying Ix yl > 6 for any x,y e

(9) (a) Let 6 > 0 and let E (2 [a,b] be a set of points satisfying Ix yl > 6 for any x,y e E. Show that the cardinality of E is less than or equal to 6" - (b a). (b) We say that a point x E E is \"isolated in E\" if there exists a 6 2* 0 such that Ix yl > 6 for every y E E \\ {x}. Prove that if E C R contains only points that are isolated in E, then E is countable

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!

Miller-Rabin test to check whether a number N is composite. This will involve computing a N1 mod N for some value of a. [10 marks] Carry out the steps for N = 65 and a = 1, 2, 8 and 12. on what each...

Provide an appropriate query to show that the above program can give an incorrect result. [4 marks] (b) Explain the cause of the error. [6 marks] (c) Suggest a correction. [5 marks] (d) Write a...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Solve the all....with Right answers Question 2 Consider a finite society ] = {1,..., I), where the preferences of the individuals are repre- sented by the utility functions (ul : R4 - R)iej. Assume...

Draw a total setup outline and decide the expense for the most economical design, i.e., the one where the complete expense of the correspondences circuits and equpment is the least. (b) The...

Steps to Step 1 2 5 6 7 8 9 m: Instructions Start Excel. Open exploring ecap_grader_c2_Transactions.xlsx and save the workbook as exploring_ecap_grader_c2_Transactions_LastFirst. On the June Totals...

unit II q12. Summarized on the right is the sale (in thousands) of the top five products in 2002. Use this information to calculate what percent of the sales of these five products was due to product...

MATH 115 Precalculus Fall, 2017, V3.4 MATH 115 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a...

. solve the attachments Assume that a five-year, government-issued coupon bond at par value NOK 100,000 and 10% coupon rate was issued today. The bond pays one annual coupon at the end of each year,...

Math 104A Homework #2 Instructor: Lihui Chai General Instructions: Please write your homework papers neatly. You need to turn in both full printouts of your codes and the appropriate runs you made....

The new manager of a theater would like to offer discounts to increase the number of tickets sold for shows on Monday and Tuesday evenings. She uses a sample of 30 weeks to record the number of...

Hierarchical clustering algorithms require O(m2 log(m)) time, and consequently, are impractical to use directly on larger data sets. One possible technique for reducing the time required is to sample...

Which of the following statements is false? multiple choice 1 Variable costs change, in total, as the level of activity changes. Variable costs are constant on a per unit basis. Average fixed cost...

In its proposed 2017 income statement, Flint Corporation reports income before income taxes $473,000, income taxes $80,410 (not including unusual items), loss on operation of discontinued music...