Prove proposition 2.3. Let f: X Y be continuous. f (X) is compact if X

Question:

Prove proposition 2.3.
Let f: X → Y be continuous.
• f (X) is compact if X is compact
• f (X) is connected if X is connected

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 11:39 AM

See More Questions

Prove proposition 3.2 assuming that X is finite-dimensional as follows: Let B be the unit ball in X, that is, B = {x: ||x|| < 1} The boundary of B is the unit sphere S = {x: ||x|| < 1}. Show that 1....
Let f: [a, b] x [c, d] R be continuous and suppose D 2 f is continuous. Define f (y) = ba f (x, y) dx. Prove Leibnitz' Rule: f1 (y) = ba D2 f (x, y) dx.
Let V Î¸ be open in R2. A function F: V R2 is said to be conservative on V if and only if there is a function f : V R such that F = f on V. Let (x, y) V and let F = (P, Q) : V R2 be...
For Questions consider the S-N curve provided below for this same material and situation. Stress & (MPa) 400 300 B. 175 MPa C. 200 MPa 200 100 10 C. 350 MPa D. 400 MPa E. It will never fail P-0.99...
In 1895, Ignaz Schwinn and his partner, Adolph Arnold, incorporated the Arnold, Schwinn & Company in Chicago to produce bicycles. In the early years with bicycle products such as the "Roadster," a...
Critical Thinking Some countries have been critical of the exporting of American culture by U.S. businesses. What about American culture might be objectionable? Can you think of some products that...
Describir los elementos del proceso de la toma de decisiones de la promocin . OA5
A U.S.-based MNC has a subsidiary in France (local currency, euro, ¬). The balance sheet and income statement of the subsidiary follow. On December 31, 2112, the exchange rate is US$1.20/¬....
Kristi had a business building destroyed in an earthquake. The old building was purchased for $251,500, and $80,300 of depreciation deductions had been taken. Her insurance proceeds were $550,750....
(a) Calculate the force exerted by the muscle and the compression force on the fifth lumbar vertebra in Fig. 1.16. Use the information provided in the text. (b) Repeat the calculations in (a) for the...
Let be a continuous preference relation on n+. Assume that is strongly monotonic. There exists a continuous function u: n+ which represents the preferences.
Suppose that X is compact and f is a continuous one-to-one function from X onto Y. Then f is an open mapping, which implies that f -1 is continuous and f is a homeomorphism.
The ledger of Hubbard Company includes the following accounts. Explain why each account may require adjustment. (a) Prepaid Insurance. (b) Depreciation Expense. (c) Unearned Service Revenue. (d)...
At March 31, account balances after adjustments for Vizzini Cinema are as follows: Account Balances Accounts Cash Supplies Equipment (After Adjustment) $11,000 4,000 50,000 Accumulated...
2. "A student holds a thin aluminum pie pan horizontally 2 m above the ground and releases it. Using a motion detector, she obtains the graph shown in Figure P3.12. Based on her measurements, (a)...
Mark has two sticks, 25 inches, and 20 inches. If he places them end-to-end perpendicularly, what two acute angles would be formed when he added the hypotenuse?
A wedding website states that the average cost of a wedding is $29,205. One concerned bride hopes that the average is less than reported. To see if her hope is correct, she surveys 36 recently...
2. (10 pts each) Use partial fractions decomposition and the tables to find the inverse z- transform of each of the following: a. X(z)= 6z-z z3-4z2-z+4 4z2 b. G(z)=- (z-1) (z-0.5) 3z +1 c. X(z) =...
Assume the market value at the end of the period (replacement cost) is $8. How might you bring this information into the reporting?
CLASS PERIO Solving Linear Equations: Variable on Both Sides Solve each equation. 1) 6r+ 7 = 13 + 7r 3) -7x-3x+2=-8x-8 5)-14 +66+7-26=1+5b 7) n-3n = 14-4n 2) 13-4x=1-x 4)-8-x= x - 4x 6)n+2=-14-n 8)...
Construct a histogram with 10 bins for the overall distance data in Exercise 6-25. Comment on the shape of the histogram. Does it convey the same information as the stem-and leaf display?
Construct a histogram for the semiconductor speed data in Exercise 6-26. Comment on the shape of the histogram. Does it convey the same information as the stem-and leaf display?
Construct a histogram for the pinot noir wine rating data in Exercise 6-27. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display?
The predetermined overhead rate is usually calculated Group of answer choices At the end of each year At the beginning of each month At the beginning of the year At the end of the month
ajax county collects property taxes for the cities within the county, Ajax county collected 1000 from citizens in Beatty city that belong to Beatty city what would be the appropriate entries for ajax...
Assume that gasoline costs $ 3 . 2 0 per gallon and you plan to keep either car for six years. How many miles per year would you need to drive to make the decision to buy the hybrid worthwhile,...

Prove proposition 2.3. Let f: X Y be continuous. f (X) is compact if X

Question:

Step by Step Answer:

Assume is compact Let be a sequence in There exists a sequence in with Since is compact it ...View the full answer

Foundations of Mathematical Economics

Students also viewed these Numerical Analysis questions