X and Y are topological spaces. is said to be open if for every open set of , the set is an open set of Y. Show projections and are open maps.
I have no idea what I need to do.
Mathematics itself is largely "all about definitions". I once had a student ask about a problem in the text (Linear Algebra). I read the problem out to the class, wrote a single word from the problem on the chalk board, and asked "what is the definition of that word". I got a lot of blank stares so I sat down at my desk, placed my hands on the desk, and waited. Eventually, the students started leafing through the book and finally one even looked up the word in the index! Once they had the precise definition of the word, they could do the problem.
Definitions in mathematics are "working definitions"- you use the precise words of the definition in proofs and problems.