So what do you think? Since the only elements of that get collapsed to the same point as are points of I think you can conclude that and so is open by definition. Now, suppose that is open, then you have that is open, but what does this set look like? Now, suppose that you had a closed set containing , then is an open set not containing and so is not an open set containing . So, what do the intersetion of all those sets look like?