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?
One of the major activities of the City Art Museum (CAM) is a Neighborhood Outreach Program, which was developed both as a public service and to market the museum and its other programs. One of the...
What do the developers gain?
Gail McCook, the administrative assistant of a local CPA firm, merged the files listing GAAS standards and GAGAS standards. Because the firm performs both GAAS and GAGAS audits, it is important to...
The following selected transactions were completed by Interlocking Devices Co., a supplier of zippers for clothing: 2017 Dec. 10. Dec. 31. Received from Unitarian Clothing & Bags Co., on account, a...
1 Without discounting cash flows to take into account the time value of money, how soon will MBC break even on the following customers? In all cases, assume that revenues and variable costs to staff...
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...
Discuss the advantages of shelf registration. What kinds of securities are most likely to be registered this way?
Write a java program that contain two overloaded methods that accepts two numbers or two characters representing a range example (11, 37) or (c, w) inputted by the user. The method generates a random...
Maggie could not conceive a child using natural means, so she sought out a woman who would donate an egg to be surgically implanted in Maggie. Which of the following items are deductible by Maggie in...
M corporation is subject to tax only in state b state b law provides for the use of federal taxable income before net operating loss and special deductions as the starting point for computing state...
Use Routh Criteria to determine the values of K needed for the system represented by the Characteristic Equation to be stable. (1 + K)s + (2K + 3)s + 2 3K = 0 Obtain the root locus plot for the...
Q7 a) Two forces equal to 2P and P act on a particle. If the first be doubled and second is increased by 12N, the direction of resultant remains unaltered. Find the value of P (5)
Schaeffer boarded a 30-passenger, single-aisle turboprop airplane carrying two pieces of baggage. When asked by a flight attendant to surrender one carry-on for proper storage, he refused and became...
5. Convert the following ERD to a relational model. SEATING RTABLE Seating ID Nbr of Guests Start TimeDate End TimeDate RTable Nbr RTable Nbr of Seats RTable Rating Uses EMPLOYEE Employee ID Emp...
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?...
4) Read the following case carefully and answer the given questions. You have been the finance director of a clothing retailer for ten years. The companys year end is 31st December 2019, and you are...
all of the other problems here on chegg don't describe right on how they god the answer. can you make it step by step math to show how you got what and from where and each number to get the answer...
D Required information The following Information applies to the questions displayed below.) Diego Company manufactures one product that is sold for $76 per unit in two geographic regions-the East and...

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