Let f: X Y be uniformly continuous. If (xn) is a Cauchy sequence in X,(f(xn) is

Question:

Let f: X → Y be uniformly continuous. If (xn) is a Cauchy sequence in X,(f(xn) is a Cauchy sequence in Y.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Foundations of Mathematical Economics

ISBN: 978-0262531924

1st edition

Authors: Michael Carter

See More Books

Question Posted: May 02, 2016 11:40 AM

See More Questions

Suppose that E X and that f : E Y. (a) If f is uniformly continuous on E and xn E is Cauchy in X, prove that f(xn) is Cauchy in Y. (b) Suppose that D is a dense subspace of X (i.e., that D X and ...
Let (xm) be a Cauchy sequence in a normed linear space x of dimension n. Let {x1,x2,...,xn} be a basis for X. Each term x''' has a unique representation 1. Using lemma 1.1, show that each sequence of...
Generalize the preceding exercise to any Hilbert space. Specifically, let S be a nonempty, closed, convex set in Hilbert space X and y B S. Let Then there exists a sequence (xn) in S such that || xn...
Introduction to Accounting An Integrated Approach EighthEdition Chapter 5 P5.10 P5.10 Engelhaupt Company is considering a switch to JIT. It has gathered the following data: In addition, Engelhaupt...
A study was conducted to determine the impact of a major Mexican peso devaluation on U.S. border retailers. As a part of the study, data were gathered on the magnitude of business that U.S. border...
Explain some of the strategies and tactics that a firm can use to enter global markets.
17-12. Cmo han cambiado las agencias de publicidad para facilitar el uso de los programas de IMC ?
Per GASB standards if a government gives a cash advance to a grantee and the grantee has not yet satised all eligibility requirements, the government would offset its credit to cash with a debit to...
Perpetual inventory using FIFO The following units of a particular item were available for sale during the calendar year: 4,500 units et jan. 1 tnventory 1 $41 Apr 19 Sale 2,200 units 4,600 units at...
6. Alumco manufactures aluminum sheets and aluminum bars The maximum production capacity is estimated at either 800 sheets or 600 bars per day. The maximum daily demand is 550 sheets and 580 bars....
Let X be any set. Let F(X) denote the set of all functions on X. Show that F(X) is a linear space.
A continuous function on a compact domain is uniformly continuous. In economic analysis, uniform continuity typically takes a slightly stronger form. A function f: X Y is Lipschitz (continuous) if...
Which of the following would increase quantity supplied, decrease quantity demanded, and increase the price that consumers pay? a. The imposition of a binding price floor b. The removal of a binding...
As an official sponsor of the Olympics, what specific benefit did John Hancock use to help drive sales in their national offices?
assumes that Nia has both a discount rate of zero and faces an interest rate of zero. These assumptions made calculating her constant level of consumption expenditure of $56,000 fairly...
Paul Petersen lives in Northern California. He owns a BMW car worth about $20,000. He wants to take a trip to Nevada with his girlfriend Patricia, who lives in Los Angeles. He takes his car into...
Do you see gendered patterns of interaction in personal relationships? Does knowing about gender linked patterns affect how other interpret on what happens in a relationships?
Significance For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are significantly high (or at least 2 standard...
Which out of the following is true about legal entity concept with regard to a sole enterprise? (a) Entity of owner is separate from the business enterprises. (b) Entity of owner and of the business...
The Taylor's series expansion for cosx about x = 0 is given by: where x is in radians. Write a user-defined function that determines cosx using Taylor's series expansion. For function name and...
Reconsider the data from Exercise 6-76. Prepare comparative box plots for two groups of observations: the first 40 and the last 40. Comment on the information in the box plots.
The data shown in Table 6-7 are monthly champagne sales in France (1962-1969) in thousands of bottles. (a) Construct a time series plot of the data and comment on any features of the data that are...
A manufacturer of coil springs is interested in implementing a quality control system to monitor his production process. As part of this quality system, it is decided to record the number of...
exercise 4-7 (Algo) Effects of transactions on income statement LO P2
Compute the value of ordinary bonds under the following circumstances assuming that the coupon rate is 0.06:(either the correct formula(s) or the correct key strokes must be shown here to receive...
A tax-exempt municipal bond has a yield to maturity of 3.92%. An investor, who has a marginal tax rate of 40.00%, would prefer and an otherwise identical taxable corporate bond if it had a yield to...

Let f: X Y be uniformly continuous. If (xn) is a Cauchy sequence in X,(f(xn) is

Question:

Step by Step Answer:

Choose some 0 Since is uniformly continuous there exists some ...View the full answer

Foundations of Mathematical Economics

Students also viewed these Numerical Analysis questions