Question

(4) Show that a totally bounded set is bounded. Is the converse true?

(4) Show that a totally bounded set is bounded. Is the converse true?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show directly that a compact metric space is totally bounded
Show directly that a compact metric space is totally bounded
Prove that X is totally bounded if every sequence of X has a convergent subsequence. Please...
Prove that X is totally bounded if every sequence of X has a convergent subsequence. Please directly prove it without using any theorem on totally boundedness.
14. Show that if a set E has positive outer measure, then there is a bounded...
14. Show that if a set E has positive outer measure, then there is a bounded subset of E that also has positive outer measure.
Suppose f is differentiable on a bounded interval (a,b) but f is unbounded there. Prove that...
Suppose f is differentiable on a bounded interval (a,b) but f is unbounded there. Prove that f' is also unbounded in (a,b). Is the converse true?
Using the completeness axiom, show that every nonempty set E of real numbers that is bounded...
Using the completeness axiom, show that every nonempty set E of real numbers that is bounded below has a greatest lower bound (i.e., inf E exists and is a real number).
A set of reals is totally disconnected if and only if it contains at least two...
A set of reals is totally disconnected if and only if it contains at least two points but no interval.
Consider the set D which is the triangular region bounded by y=x, x=0, y=4 and the...
Consider the set D which is the triangular region bounded by y=x, x=0, y=4 and the boundary of this triangular region. Find the absolute maximum and minimum values of f(x,y) = x2 -xy +y2+1 on D. Make sure you show work for testing for critical values inside the region and on the lines that make up the boundary as part of your work shown
Prove: Let S be a bounded set of real numbers and let a > 0. Define...
Prove: Let S be a bounded set of real numbers and let a > 0. Define aS = {as : s ∈ S}. Show that inf(aS) = a*inf(S).
Determine either True or False: 1. 0 is an element to null set. 2. {1} element...
Determine either True or False: 1. 0 is an element to null set. 2. {1} element of {1,2,3}. 3. ~ q implies ~ p is the converse of ~ p implies ~ q . 4. She is unhappy is a primitive proposition. 5. ~ p implies q is logically equivalence with p implies q .
Consider the region bounded by ? = 4? , ? = 1 and x-axis. Set up...
Consider the region bounded by ? = 4? , ? = 1 and x-axis. Set up the appropriate integrals for finding the volumes of revolution using the specified method and rotating about the specified axis. Be sure to first sketch the region and draw a typical cross section. SET UP THE INTEGRALS ONLY. DO NOT evaluate the integral. a) Disc/washer method about the x-axis b) Shell method about the y-axis c) Disc/washer method about the line ? = 2. d)...