Topology Problems

Question

(4) For this problem only the topology T on R will consist of φ, R and all open intervals E = (a, ∞) where a ∈ R.
(a) Determine the closed subsets of (R, T)
(b) Determine the limit points and the closure of each set below.
(Recall that the closure of a set is the smallest closed set containing that set.)
(1) [3, 7) (half-open interval)
(2) {7, 24, 47, 85}
(3) {3, 6, 9, 12, ...}

Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.