Assignment:
Which of the following topological spaces is normal?
a) Reals with the "usual topology."
b) Reals with the "finite complement topology:" U open in X if U - X is finite or is all of X.
c) Reals with the "countable complement topology:" U open in X if X - U is countable or is all of X.
d) Reals with the "lower limit topology:" basis half-closed intervals [a,b)
e) Reals with the "upper limit topology:" basis half-closed intervals (a,b]
f) Reals with the "K-topology:" basis consists of open intervals (a,b) and sets of form (a,b) - K where K = {1, 1/2, 1/3, ... }
Provide complete and step by step solution for the question and show calculations and use formulas.