Question

Show there does not exist a sequence of continuous functions fn : [0,1] → R converging...

Show there does not exist a sequence of continuous functions fn : [0,1] → R converging pointwise to the function f : [0,1] → R given by f(x) = 0 for x rational, f(x) = 1 for x irrational.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show there does not exist a sequence of polynomials converging uniformly on R to f if...
Show there does not exist a sequence of polynomials converging uniformly on R to f if f(x)=cosx
Problem 3. Consider a sequence for functions fn : [0, 2] → R such that f(0)...
Problem 3. Consider a sequence for functions fn : [0, 2] → R such that f(0) = 0 and f(x) = (sin xn)/(xn) for x ∈ (0, 2]. Find limn→∞ ∫[0,2] fn(x) dx
Does there exist a continuous onto function f : [0, 1] → R? Does there exist...
Does there exist a continuous onto function f : [0, 1] → R? Does there exist a continuous onto function f : (0, 1) → (−1, 0) ∪ (0, 1)?
Find a sequence of positive Lebesgue integrable functions on [0,1] which do not converge pointwise (it...
Find a sequence of positive Lebesgue integrable functions on [0,1] which do not converge pointwise (it means that there is no point x0 so that fn(x0 ) is a convergent sequence) but its integrals do converge to zero.
Real analysis conception If the sequence of function fn is continuous, does that means its subsequence...
Real analysis conception If the sequence of function fn is continuous, does that means its subsequence fnk is also continuous? if the sequence of function gn is equicontinuous , does that mean the subsequence gnk is equicontinuous?
Real Analysis: Suppose f: [0,1] --> R is continuous, and {xn} is a Cauchy sequence in...
Real Analysis: Suppose f: [0,1] --> R is continuous, and {xn} is a Cauchy sequence in [0,1]. Prove or disprove that {f(xn)} is a Cauchy Sequence.
Let C [0,1] be the set of all continuous functions from [0,1] to R. For any...
Let C [0,1] be the set of all continuous functions from [0,1] to R. For any f,g ∈ C[0,1] define dsup(f,g) = maxxE[0,1] |f(x)−g(x)| and d1(f,g) = ∫10 |f(x)−g(x)| dx. a) Prove that for any n≥1, one can find n points in C[0,1] such that, in dsup metric, the distance between any two points is equal to 1. b) Can one find 100 points in C[0,1] such that, in d1 metric, the distance between any two points is equal to...
If R is the ring of all real valued continuous functions defined on the closed interval...
If R is the ring of all real valued continuous functions defined on the closed interval [0,1] and if M = { f(x) belongs to R : f(1/3) = 0}. Show that M is a maximal ideal of R
Let f: (0,1) -> R be uniformly continuous and let Xn be in (0,1) be such...
Let f: (0,1) -> R be uniformly continuous and let Xn be in (0,1) be such that Xn-> 1 as n -> infinity. Prove that the sequence f(Xn) converges
show that a sequence of measurable functions (fn) converges in measure if and only if every...
show that a sequence of measurable functions (fn) converges in measure if and only if every subsequence of (fn) has subsequence that converges in measure
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT