Suppose that Y is compact. f: X Y is continuous if and only if graph(f) =

Question:

Suppose that Y is compact. f: X → Y is continuous if and only if graph(f) = {(x, y): y = f(x),x ∊ X} is a closed subset of X × 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 11:39 AM

See More Questions

Suppose that Y is compact. The correspondence
A closed subset of a compact set is compact.
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 following is information for Palmer Company. \ table [ [ , Year,Year 2 , Year 1 ] , [ Cost of goods sold,$ 6 3 3 , 8 2 5 , $ 4 1 6 , 6 5 0 , $ 3 8 1 , 3 0 0 The following is information for...
A process produced good parts and defective parts. A sample of 60 parts was taken and inspected. Eight defective parts were found. The sequence of good and defective parts was analyzed by using...
Sue owns a vacation home. Will her cousin's free personal use of the home be considered as "personal use" by Sue for purposes of the vacation home deduction rules?
Show that, for irrotational axisymmetric flows in cylindrical coordinates, the streamfunction satisfies the following equation: \[\frac{\partial^{2} \psi}{\partial r^{2}}-\frac{1}{r}...
X plc manufactures Product X using three different raw materials. The product details are as follows: It is company policy to hold stocks of finished goods at the end of each month equal to 50 per...
Given the following Venn diagram, find n[(CUB)]. 11 10 10 15 15 6 12 5 11 B U
a. Find the z-value for a trip that takes 66.1 min. b. Find the z-value for a trip that takes 55 min. c. Find the probability that the bus trip takes between 55 and 66.1 min.
If f is a continuous function from X to Y, the graph of f, graph(f) = {x, y) : y = f (x), x X} is a closed subset of X Y. The converse of this result is not true in general. The following exercise...
If f: X Y and g: Y Z are continuous function, so is their composition g o f: X Z.
Find the critical value t c for the level of confidence c and sample size n. c = 0.90, n = 10
What is management audit?
What is periodical audit? What are the advantages and disadvantages of periodical audit? Distinguish between continuous audit and periodical audit.
(a) Distinguish between internal audit and statutory audit. (b) Can the statutory auditor rely upon the internal audit in carrying out his function as a statutory auditor?
Explain the following statement (a) Vouching is the essence of auditing. (b) In vouching payments, the auditor does not merely seek proof that money has been paid away.
What precautions are to be taken in the application of internal check system?
The controller of Ephraim, Inc. has computed quality costs as a percentage of sales for the past 5 years (20X1 was the first year the company implemented a quality improvement program). This...
What are the main distinctions between the different schools of legal interpretation?
A Comparative Stem-and-Leaf Diagram in Exercise 6-22, we presented height data that was self-reported by female undergraduate engineering students in a core course at ASU. In the same class, the male...
Construct a frequency distribution and histogram for the motor fuel octane data from Exercise 6-14. Use eight bins.
Construct a frequency distribution and histogram using the failure data from Exercise 6-15.
. For each of these relations, write down all functional dependencies. If there are no functional dependencies among attributes, you must state so. Do not write down trivial functional dependencies,...
and b = 3. 7.3a=2*b 8.(5-a)*b <7 9.b
What diameter of vertical tube would allow mayonnaise (= 1,200 kg/m3) to flow under its own weight?

Suppose that Y is compact. f: X Y is continuous if and only if graph(f) =

Question:

Step by Step Answer:

By the previous exercise continuous implies graph closed Con...View the full answer

Foundations of Mathematical Economics

Students also viewed these Numerical Analysis questions