In this paper, we investigate some properties of Khalimsky topological spaces. More precisely, we investigate topological properties of the Khalimsky line. After observing that the Khalimsky line is not compact, we construct the one point compactification of the Khalimsky topological line, compare this with the Khalimsky line. Constructing the quotient topology using the equivalence relation on the Khalimsky line, we investigate its topological properties. Especially, we introduce both a particular topology and an excluded point topology. Finally, we study some properties of the quotient topology of the Khalimsky line constructed in terms of a special kind of method.