I'm trying to get my head around Borel sets (like so many before me!) IF I've understood them correctly, the definition on http://en.wikipedia.org/wiki/Borel_set seems unnecessarily complicated. Isn't the following equivalent?
If for all x in A all values in the neighbourhood of x are also in A (in one direction, if x is the end of a closed interval) then A is a Borel set.
If this is not correct, what have I misunderstood?