Let us first look at the points of a topological space "X". One is usually tempted to consider a point of "X" as an element "x" of the set "X", but there is in fact a more useful description for our current investigation. Any point "x" gives rise to a continuous function "p""x" from the one element topological space 1 (all subsets of which are open) to the space "X" by defining "p""x"(1) = "x". Conversely, any function from 1 to "X" clearly determines one point: the element that it "points" to. Therefore, the set of points of a topological space is equivalently characterized as the set of functions from 1 to "X".