Suppose that Va aA is a collection of nonempty open sets in X which satisfies Va V for all a in A Prove that if X is separable, then A is countable What happens to this result when open is omitted ...

Suppose A is uncountable Since each V is nonempty ch ...

Suppose that {Va}aA is a collection of nonempty open sets in X which satisfies Va V

Question:

Suppose that {Va}a∈A is a collection of nonempty open sets in X which satisfies Va ∩ Vβ = θ for all a ≠ β in A. Prove that if X is separable, then A is countable. What happens to this result when open is omitted?

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

Step by Step Answer:

Related Book For book-img-for-question

An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

See More Books

Question Posted: Mar 29, 2016 04:17 AM

See More Questions

Suppose that {Va}aA is a collection of nonempty open sets in Rn which satisfies Va V = for all in A. Prove that A is countable. What happens to this result when open is omitted?
Let {S1, S2,..., Sn} be a collection of nonempty (possibly non convex) subsets of an m-dimensional linear space, and let Then 1. 2. where 3. with bij ¥ 0 and bij > 0 for at most m + n components....
Let {S1, S2, . . . , Sn} be a collection of nonempty compact subsets of an m-dimensional linear space, and let x conv We consider the Cartesian product of the convex hulls of Si, namely Every point...
Use the following transactions to answer the questions. Use a 6% sales tax rate. Total and rule the sales journal. Jan. 3 Sold merchandise on account to J. J. Johnson, $1,500, plus sales tax. 7 Sold...
Given the following information, prepare in good form an income statement for Jonas Brothers Cough Drops. Selling and administrative expense $ 328,000 Depreciation expense 195,000 Sales 1,660,000...
Prepare an unadjusted trial balance, in correct format, from the following alphabetized account information. Assume accounts have normal balances. Accounts payable Accounts receivable Cash Common...
Identify for an employee (perhaps yourself) what knowledge he/she creates, acquires, captures, shares and uses while doing a specified task.
Colorado Telecom, Inc. manufactures telecommunications equipment. The company has always been production oriented and sells its products through agents. Agents are paid a commission of 15 percent of...
All info given. Required information (The following information applies to the questions displayed below.] Williams Company is a merchandiser and its accounting department has finished preparing a...
Multitasking is common in the workplace but does it make employees more efficient and effective pretend you're the manager in charge of a loan processing department describe how you would research...
Suppose that E R is compact and nonempty. Prove that sup E, inf E E.
Prove that if V is open in a separable metric space X, then there are open balls B1, B2,... such that Prove that every open set in R is a countable union of open intervals. jEN
In Exercises: a) Find the discriminant b 2 - 4ac, and then determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist. b) Solve...
Problem 228: The derivative is dz dt = = atb where a , and b =
Write a Python program which will take N names from the user. Create a dictionary from the N names that will hold First_name, Middle_name and Last_name in separate keys. The inputs will take N at...
2 Finding Poles and Zeros from a Bode Plot Consider the magnitude portion of the Bode plot in Figure 3. Based on the linear approxi- mation in red, find the transfer function G(s). 5 0 -5 10 -10 -15...
Indicate whether the following statements are "TRUE" or "FALSE" 1- Financial accounting is considered to be the backbone to top management. 2- Cost accounting identifies, summarizes and interprets...
Refer to case 3 shown above. Assume that Beta Division is now receiving an 3% price discount from the outside supplier. a. What is Alpha Division's lowest acceptable transfer price? b. What is Beta...
An innkeeper is the operator of a hotel, motel, or inn that holds itself out to the public as being ready to entertain travelers, strangers, and transient guests. True/False
Write out the formula for the total costs of carrying and ordering inventory, and then use the formula to derive the EOQ model. Andria Mullins, financial manager of Webster Electronics, has been...
An article in the Journal of Aircraft (Vol. 23, 1986, pp. 859864) describes a new equivalent plate analysis method formulation that is capable of modeling aircraft structures such as cranked wing...
Ten individuals have participated in a diet-modification program to stimulate weight loss. Their weight both before and after participation in the program is shown in the following list is there...
Two different analytical tests can be used to determine the impurity level in steel alloys. Eight specimens are tested using both procedures, and the results are shown in the following tabulation. Is...
If the auditor believes that the financial statements prepared on the basis of the entity's income tax are not adequately titled, the auditor should : A)Issue a resignation of opinion. B)Explain the...
initial stock offering to the public. This REIT specializes in the acquisition and management of warehouses. Your firm, Blue Street Advisors, is an investment management company that is considering...
Question 3 You have been hired to run a pension fund for Mackay Inc, a small manufacturing firm. The firm currently has Gh5 million in the fund and expects to have cash inflows of $2 million a year...

Suppose that {Va}aA is a collection of nonempty open sets in X which satisfies Va V

Question:

Step by Step Answer:

Suppose A is uncountable Since each V is nonempty ch...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions