A nontrivial pairing of finite T0 spaces

There is a four-point space S1 weakly homotopy equivalent to the circle. The restriction to S1 of the complex number multiplication is not continuous, nevertheless a continuous model of the multiplication with values in S1 can be defined on an eight-point circle. Applying an analogue of Hopfʹs construction we obtain a finite model of Hopfʹs famous map S3→S2.