I am not sure if i understood you well (as I'm not very much familiar with topology)
What I am trying to ask is the following: convex functions on R generate the fine topology and convex functions on R are the continuous functions so obviosly they generate the same topology. But since on...
yes i mean the same topology.
Convex functions on [0,1] are discontinuous at the boundaries so I don't understand how they generate the same topology as continuous functions.
Can anyone please help me with this because I'm really getting confused. Thanks!
In R, we know that fine topology is equivalent to the Euclidean topology as convex functions are continuous.
Now if instead of R we consider a subset of it say [0,1], the fine topology induced on [0,1] would...