Open and Closed Sets Examples
28683
Sum of two closed sets in $\mathbb R$ is closed?
148213
Given a topological space $X$, why are both $X$ and $\emptyset$ open and closed?
8015
Compact set plus a closed set is a closed set
143457
Is product of two closed sets closed?
116009
Proving that if a set is both open and closed then it is equal to the real numbers
5323
Example to show the distance between two closed sets can be 0 even if the two sets are disjoint
79424
Don't understand proof that interior of a set is open
46698
Showing a set is closed under inverses
89749
Example of a not recursively enumerable set $A \subseteq \mathbb{N}$
91991
How do I prove that two closed sets are separable?
153934
How to prove that a set R\Z is open
42145
Prove that the only sets in $R$ which are both open and closed are the empty set and $R$ itself.
39020
Why is empty set an open set?
72468
Open and closed balls in $C[a,b]$
73130
A simple question about open set
63701
An example of a regular function over an open set
3663
Finding counterexamples in elementary set theory.