Equicontinuity

**orbit** · May 15th 2011, 05:26 PM

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

Let f and g $\in$ C(X,F)

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

I really dont know where to start....

**Drexel28** · May 15th 2011, 07:35 PM

Originally Posted by orbit

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

Let A anb B $\in$ 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.

**orbit** · May 15th 2011, 08:52 PM

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)

**Jose27** · May 15th 2011, 09:15 PM

Hint:

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

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

**orbit** · May 16th 2011, 06:01 AM

Originally Posted by Jose27

Hint:

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

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

Thank you.

For 2) is the same delta for 1??

Regars.

**orbit** · May 16th 2011, 07:55 PM

I finished the exercise.

Thank u!

Thread: Equicontinuity

LinkBack

Thread Tools

Display

Equicontinuity

Similar Math Help Forum Discussions

Equicontinuity implies Uniform Equicontinuity

Equicontinuity Question

Equicontinuity

Uniform convergence and equicontinuity

need help with two (basic?) proofs involving equicontinuity

Search Tags