Let T be the collection of subsets of R consisting of the empty set and every set whose complement is countable.
a) Show that T is a topology on R.
b) Show that the point 0 is a limit point of the set A= R - {0} in the countable complement topology.
c) Show that in A = R -{0} there is...
We defined the closure of a subset A of a topological space as the intersection of all closed sets containing A. We basically want to find the smallest closed set containing A for closure.
Prove that Cl(Q) = R in the standard topology
I'm really stuck on this problem, seeing as we haven't covered limit points yet in the text and are not able to use them for this proof. Can anybody provide me with help needed for this proof? Many thanks.