Determine whether the following are subspaces of C[-1,1]:

(c) The set of continous nondecreasing functions on [-1,1]

Question

Determine whether the following are subspaces of C[-1,1]:

(c) The set of continous nondecreasing functions on  [-1,1]

anonymous · Answer

Define the operations on the vector space?

kinggeorge · Answer

We need to show three things to be a subspace. 
1. It has the 0 function, 
2. Closed under function composition,
3. Closed under scalar multiplication. 

However, if you take an increasing function, and multiply it by -1, then you have a decreasing function. Therefore, it's not a subspace.

anonymous · Answer

What George said. It would include the 0. It would be closed under addition. It would not be closed under scalar multiplication.