Test Your Intuition 60: The Finite and Infinite Borsuk’s Conjecture

Let f(d) be the smallest integer so that every set of diameter one in can be covered by f(d) sets of smaller diameter. Let g(d) be the smallest integer so that every finite set of diameter one in can be covered by g(d) sets of smaller diameter. Clearly g(d) ≤ f(d) Test your intuition: Is g(d)=f(d) ?