Give examples of maps between subsets of the plane (with Euclidean toplogy) that are:
a) open but not closed or continuous
b) closed but not open or continuous
c) continuous and open but not closed
e) continuous and closed but not open
f) open and closed but not continuous
The Attempt at a Solution
So i just want to get this thread up now and then update it as I work on each of these individually.... I have a few thoughts so far
e) How about a map R^2-->R^2 that sends each basis element to it's closure?
c) Maybe a map R^2--->R^2 that sends the closure of each basis element to it's interior?
I will think about this more and post more ideas for the other ones... If anyone could critique what I have thought of so far I'd appreciate it :D.