1. The problem statement, all variables and given/known data Let ℝ be set of real numbers. Which of the following collection of subsets of ℝ defines a topology in ℝ. a) The empty set and all sets which contain closed interval [0,1] as a subset. b)R and all subsets of closed interval [0,1]. c)The empty set, ℝ and all sets such that A not subset of [0,1] and [0,1] not subset of A. Determine if obtained topology is connected and Hausdorff. 3. The attempt at a solution Im not sure how to interpret subsets of the closed interval [0,1] and this doesnt seem like it would be an open set.