Let H X. Prove that H is compact if and only if every cover {Ea)aA of

Question:

Let H ⊂ X. Prove that H is compact if and only if every cover {Ea)a∈A of H, where the Ea's are relatively open in H, has a finite subcover.

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

Let H Rn. Prove that H is compact if and only if every cover {Ea}aA of H, where the E's are relatively open in H, has a finite subcovering.
Let a < b < c. Suppose that f is continuous on [a, b], that g is continuous on [b, c], and that f (b) = g(b). Define h on [a, c] by h(x) := f(x) for x |a, b and h(x) := g(x) for x |b, c. Prove that...
Let X be a compact metric space. A closed subspace of C(X) is compact if and only if it is bounded and equicontinuous.
Which of the following represents the GREATEST risk created by a reciprocal agreement for disaster recovery made between two companies? A. Developments may result in hardware and software...
What is the difference between book value per share of common stock and market value per share? Why does this disparity occur?
Explain how goal setting motivates an individual, and review the four practical lessons from goal-setting research.
Do the assumptions for Bernoulli trials appear to hold? Explain. If the assumptions hold, identify success and the probability of interest. (a) A TV ratings company will use their electronic...
Gianna Tuck is an accountant for Post Pharmaceuticals. Her duties include tracking research and development spending in the new product development division. Over the course of the past six months,...
Grouper Limited had net sales in 2023 of $2.1 million. At December 31, 2023, before adjusting entries, the balances in selected accounts were as follows: Accounts Receivable $261,300 debit; Allowance...
The following information pertains P15-8 to the pension plan of Beatty Business Group: Note that the information in Columns (2) and (3) are as of the beginning of the year, whereas the information in...
Suppose that X and Y are metric spaces and that f : X Y. If X is compact and connected, and if to every x X there corresponds an open ball Bx such that x Bx and f(y) = f(x) for all y Bx, prove...
A set E in a metric space is called clopen if it is both open and closed. a) Prove that every metric space has at least two clopen sets. b) Prove that a metric space is connected if and only if it...
Based upon your reading of Insight 1.1, conduct additional research and discuss the current policy on infectious disease quarantine and how this process is administered in the United States.
You are studying survival times for mice given a drug at one of three doses (Low, Medium, or High). You define two dummy variables: (a) With these definitions, write the expressions for the mean...
In science experiments, a very small value of the 2 statistic (one very near 0.0) is sometimes regarded with suspicion. Why?
N = 150, n = 20, k = 30 Compute the mean and standard deviation of the hypergeometric random variable X.
When listing the possible values of the hypergeometric random variable X, it must be the case that x is less than or equal to the smaller of n or k. Why?
Explain the similarities and differences between the hypergeometric probability distribution and the binomial probability distribution.
For the rectangular region shown in Figure 14.46, the electric potential is zero on the boundaries and the charge distribution v is 50 nC/m 3 . Although there are six free nodes, there are only four...
-4 1 9. Let A = Find A-1, (A") and verify that (A")= (A-1)".
Consider the fire-fighting foam expanding agents investigated in Exercise 10-18, in which five observations of each agent were recorded. Suppose that, if agent 1 produces a mean expansion that...
A fuel-economy study was conducted for two German automobiles, Mercedes and Volkswagen. One vehicle of each brand was selected, and the mileage performance was observed for 10 tanks of fuel in each...
Reconsider the fuel-economy study in Supplemental Exercise 10-83. Rework part (d) of this problem using an appropriate hypothesis-testing procedure. Did you get the same answer as you did originally?...
Thank you for your phone call this morning. As agreed, I am emailing you regarding the two following accounting issues (listed below). As I do not have any accounting experience, please explain the...
discuss the ethical dimensions of organizational culture, including the role of ethical leadership, moral values, and ethical decision-making frameworks in promoting a culture of integrity,...
Windsor Company adopted a stock-option plan on November 30, 2024, that provided that 67,900 shares of $5 par value stock be designated as available for the granting of options to officers of the...

Let H X. Prove that H is compact if and only if every cover {Ea)aA of

Question:

Step by Step Answer:

Suppose H is compact Let U A be a relatively open covering o...View the full answer

An Introduction to Analysis

Students also viewed these Numerical Analysis questions