Sorry, my question above is not clear, here I rewrite it to be more accurate and specific:

Let A={a_{1},a_{2},...,a_{n}}, B={b_{1},b_{2},...,b_{n}} and C={c_{1},c_{2},..,c_{n-1}} be discrete finite sets embedded in a unit sphere S^2=x^2+y^2+z^2=1 so that the topologies of A,B and C are induced topology from the topology of the sphere (Note that the topologies of A, B and C are P(A), P(B) and P(C) respectively, where P(A) denotes the power set of A). Assume also that the points of B are imbedded in a great circle in S^2 such that the arc length between each two of these points is equal. Also suppose that elements of C are imbedded in a great circle (It can be same great circle of B) so that the arc length between each two of these elements is equal. Define f_{0} from A to B by f_{0}(a_{i})=b_{i} for i=1,2,...,n. Define also a function f_{1} from A to C by f_{1}(a_{1})=f_{1}(a_{n})=c_{1} and f_{1}(a_{i})=c_{i} otherwise. The question is: Is it possible to define a homotopy F from A * [0,1] to S^{2} between f_{0} and f_{1}.

Thank you in advance