1. ## Equicontinuity

Let X a metric compact space and Y a Banach Space.

Let f and g $\displaystyle$\in$$C(X,F) Prove that: 1) A+B is equicontinuous, and 2) A U B is equicontinuous I really dont know where to start.... 2. Originally Posted by orbit Let X a metric compact space and Y a Banach Space. Let A anb B \displaystyle \in$$ C(X,F)

Prove that: 1) A+B is equicontinuous, and
2) A U B is equicontinuous

I really dont know where to start....
What does this mean? Equicontinuity applies to a family of maps.

3. Originally Posted by Drexel28
What does this mean? Equicontinuity applies to a family of maps.
Hi, A and B are Equicontinuous subsets of C(X,F)

4. Hint:

1. $\displaystyle |f(x_0)-f(x)+(g(x_0)-g(x))|\leq |f(x_0)-f(x)|+|g(x_0)-g(x)| < 2\varepsilon$ if $\displaystyle |x-x_0|<\delta =\min \{ \delta _A, \delta _B \}$ whenever $\displaystyle f\in A, \ g\in B$

2. For the union use the same $\displaystyle \delta$.

5. Originally Posted by Jose27
Hint:

1. $\displaystyle |f(x_0)-f(x)+(g(x_0)-g(x))|\leq |f(x_0)-f(x)|+|g(x_0)-g(x)| < 2\varepsilon$ if $\displaystyle |x-x_0|<\delta =\min \{ \delta _A, \delta _B \}$ whenever $\displaystyle f\in A, \ g\in B$

2. For the union use the same $\displaystyle \delta$.
Thank you.

For 2) is the same delta for 1??

Regars.

6. I finished the exercise.

Thank u!