Let T consist of $\displaystyle \emptyset$,$\displaystyle \Re$ and all intervals (-$\displaystyle \infty$,p) for p$\displaystyle \in$ $\displaystyle \Re$. Prove that T is a topology on $\displaystyle \Re$
Axioms of a topology :
$\displaystyle \emptyset$ and $\displaystyle \Re$ belong to the collection.
A finite intersection of sets in the collection is in the collection.
An arbitrary union of sets in the collection is in the collection.