On Number of k-Element in Open and Clopen Topological Space With Corresponding Graph for n≤4

In this paper, we determine the number of elements defined on each topology of a topological space for open and clopen topological spaces T(n) for 1≤n≤4, which is called k-element. A graph of the relationship between topologies for open and clopen set for n≤3 are discussed. Hence; T(n,k) is clopen for n≥1 if and only if k=2n.