Question

Let f and g be continuous functions from C to C and let D be a...

Let f and g be continuous functions from C to C and let D be a dense

subset of C, i.e., the closure of D equals to C. Prove that if f(z) = g(z) for

all x element of D, then f = g on C.

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

Homework Answers

Answer #1

Kindly give a thumbs up

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
Let f, g : X −→ C denote continuous functions from the open subset X of...
Let f, g : X −→ C denote continuous functions from the open subset X of C. Use the properties of limits given in section 16 to verify the following: (a) The sum f+g is a continuous function. (b) The product fg is a continuous function. (c) The quotient f/g is a continuous function, provided g(z) != 0 holds for all z ∈ X.
Let D ⊆ R, a ∈ D, let f, g : D −→ R be continuous...
Let D ⊆ R, a ∈ D, let f, g : D −→ R be continuous functions. If limx→a f(x) = f(a) and limx→a g(x) = g(a) with f(a) < g(a), then there exists δ > 0 such that x ∈ D, 0 < |x − a| < δ =⇒ f(x) < g(x).
Let (X, d) be a metric space, and let U denote the set of all uniformly...
Let (X, d) be a metric space, and let U denote the set of all uniformly continuous functions from X into R. (a) If f,g ∈ U and we define (f + g) : X → R by (f + g)(x) = f(x) + g(x) for all x in X, show that f+g∈U. In words,U is a vector space over R. (b)If f,g∈U and we define (fg) : X → R by (fg)(x) = f(x)g(x) for all x in X,...
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...
Let f and g be continuous functions on the reals and let S={x in R |...
Let f and g be continuous functions on the reals and let S={x in R | f(x)>=g(x)} . Show that S is a closed set.
Let f(z) and g(z) be entire functions, with |f(z) - g(z)| < M for some positive...
Let f(z) and g(z) be entire functions, with |f(z) - g(z)| < M for some positive real number M and all z in C. Prove that f'(z) = g'(z) for all z in C.
Let f and g be measurable unsigned functions on R^d . Assume f(x) ≤ g(x) for...
Let f and g be measurable unsigned functions on R^d . Assume f(x) ≤ g(x) for almost every x. Prove that the integral of f dx ≤ Integral of g dx.
1. Let A = {1,2,3,4} and let F be the set of all functions f from...
1. Let A = {1,2,3,4} and let F be the set of all functions f from A to A. Prove or disprove each of the following statements. (a)For all functions f, g, h∈F, if f◦g=f◦h then g=h. (b)For all functions f, g, h∈F, iff◦g=f◦h and f is one-to-one then g=h. (c) For all functions f, g, h ∈ F , if g ◦ f = h ◦ f then g = h. (d) For all functions f, g, h ∈...
Let A, B, C be sets and let f : A → B and g :...
Let A, B, C be sets and let f : A → B and g : f (A) → C be one-to-one functions. Prove that their composition g ◦ f , defined by g ◦ f (x) = g(f (x)), is also one-to-one.
Let f : A → B and g : B → C. For each of the...
Let f : A → B and g : B → C. For each of the statements in this problem determine if the statement is true or false. No explanation is required. Just put a T or F to the left of each statement. a. g ◦ f : A → C b. If g ◦ f is onto C, then g is onto C. c. If g ◦ f is 1-1, then g is 1-1. d. Every subset of...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT