A set F is closed iff for all x_n in F for all n in the naturals (x_n) converges to l, then l is in F. (x_n) is a sequence© BrainMass Inc. brainmass.com October 9, 2019, 10:35 pm ad1c9bdddf
A closed set can have lots of equivalent definitions. This problem is one definition of a closed set. Now I use the other two equivalent definition of closed set to prove this problem.
1. The complement of a closed set is an open set.
2. Each point outside of a closed set has a disjoint neighborhood from this closed ...
This provides an example of proving a set is closed.