menu
bartleby
search
close search
Hit Return to see all results

3. Show that closed subspace of a complete metric space is complete.4. Let f be a continuous mapping of a compact metric space X to metric space Y. Prove thatf (X) is compact.A 1S

Question
3. Show that closed subspace of a complete metric space is complete.
4. Let f be a continuous mapping of a compact metric space X to metric space Y. Prove that
f (X) is compact.
A 1S
help_outline

Image Transcriptionclose

3. Show that closed subspace of a complete metric space is complete. 4. Let f be a continuous mapping of a compact metric space X to metric space Y. Prove that f (X) is compact. A 1S

fullscreen
check_circleAnswer
Step 1

As per norms, the first question is answered: To prove that a closed subspace Y of a complete metric space X is complete.

Step 2

A metric space X is complete if all Cauchy sequences in X converge in X. A subspace Y of X is closed if it containes all the limit points of sequences in Y. We need to show that Y is complete in itself (in the induced topology form X); in other words, every Cauchy sequence in Y converges in Y.

Step 3
fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Advanced Math

Related Advanced Math Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: Suppose that f(z) is an entire function such that f(z)/zn is bounded for |z|>= R. Show that f(z) ...

A: Let f(z) is an entire function such that f(z)/zn is bounded for |z|≥ R.Since f is an entire function...

question_answer

Q: pls explain to step by step and dont skip any steps. thanks

A: To anayze the behaviour of the critical points using the eigenvalues (and eigenvectors)

question_answer

Q: Let i, j be coprime positive integers, and let R be an integral domain. Prove that (r-y) is a prime ...

A: To show that the ideal generated by x^i-y^j under the given conditions is a prime ideal in the ring ...

question_answer

Q: Please answer numbers 6 and 7. Thanks,

A: 6a) The series is 

question_answer

Q: Hello, Please help me solve number 13 in the attachment. Thank you very much.

A: It is given that the function f is differentiable on the set of real numbers and let

question_answer

Q: pls explain to me step by step. thanks

A: To establish the (given) necessary and sufficient conditions for the periodicity of solutions of the...

question_answer

Q: Solve the differential equation using either the method of undetermined coefficients or Laplace tran...

A: The given equation is y″′+y″+y′+y=e^(-t)+4t.

question_answer

Q: 5. A bag of 10 apples contains 2 rotten apples and 8 good apples. A shopper selects a sample of thre...

A: (a)To calculate the possible number of samples.Given:

question_answer

Q: Derive a numerical differentiation formula of order O(h4) by applying Richard- 4. extrapolation to f...

A: Its given that:

Sorry about that. What wasn’t helpful?