Let be a topological space, where is cofinite topology on . Let us show that where is set of all neignborhoods of .
By defenition, a subset is called an open set of topological space if is an element of topology . A neignborhood of a point is an open set such that . It follows that each neignborhood of belongs to . Therefore, .
On the other hand, the set is an open set in cofinite topology on , and . Therefore,
Comments