1. Let
Find and explain.
id say that interior is empty set and closure is A, but if so, how to show that?
2. Let and . Let . i dont know how exactly its called but: is C partly opened with respect to A, or partly closed?
definition: Y is partly opened with respect to X if and only if there exists opened set such that
Well, first-off it tells you that is the intersection of the preimages of two closed sets under a continuous map, in other words it's the intersection of two closed sets, in other words it's closed, in other words
Why do you think ?
I don't understand I guess what's the problem. What you're calling "party open" just means that it's open in the subspace topology (or open as a metric subspace...whatever your prefer), in other words it's the intersection of with an open set. But, once again x,y)\mapsto x-y" alt="\varphi:\mathbb{R}^2\to\mathbb{R}x,y)\mapsto x-y" /> is continuous and ...soooo?i dont know.. B isnt closed, so C wont be closed, , is open so C is open?