We have a definition for continuity in terms of open sets of topologies, but I had a question about it. Here's the definition:
Let and be topological spaces. A function is continuous relative to and provided for every .
My question is this: Is continuous relative to and provided for every ? Or is there something else you have to do to that sentence to make it true?
The very first time I was asked to present a proof in a Graduate school class, it was precisely a problem involving where A was in the image of f. I did the whole problem assuming that f was invertible (they said " " didn't they?)!