Understanding the Co-finite Topology on R I'm looking to gain a better understanding of how the cofinite topology applies to R. 
I know the definition for this topology but I'm specifically looking to find some properties such as the closure, interior, set of limit points, or the boundary set and how these change based on whether a subset A in R is closed, open, or clopen. 
Any help would be appreciated. 
Note: I have only the most basic of definitions for closure, interior, etc. 
Thank you! 

In the cofinite topology, '$A$ is closed' means '$A$ is finite or is $\mathbb{R}$' and '$A$ is open' means '$A$ has finite complement or is empty'. In particular...


*

*If $A \subseteq \mathbb{R}$ is infinite then the only closed set containing $A$ is $\mathbb{R}$, and hence $\operatorname{cl} A = \mathbb{R}$. In particular, if $A$ is infinite, every point of $\mathbb{R} - A$ is a limit point of $A$. Hence if $A$ is infinite then $\partial A = \mathbb{R} - A$.

*If $A \subseteq \mathbb{R}$ has infinite compliment then its only open subset is $\varnothing$, so $\operatorname{int} A = \varnothing$.

*The only clopen sets are $\mathbb{R}$ and $\varnothing$.

