# The Product of Topological Spaces Does Not Obey Cancellation

Exercise 1. Find metric topological spaces $$A,B,C$$ such that $$A$$ is not homeomorphic to $$B$$, but $$A\times C$$ is homeomorphic to $$B\times C$$.

Exercise 2. Find path connected metric topological spaces $$A,B,C$$ such that $$A$$ is not homeomorphic to $$B$$, but $$A\times C$$ is homeomorphic to $$B\times C$$.