In his recent book [3] Nadler observes that the property of admitting a Whitney map is of fundamental importance in studying the internal structure of hyperspaces, especially their arc structure. Nadler presents three distinct methods of constructing a Whitney map on the hyperspace 2X of nonempty closed subsets of a continuum.

A partially ordered space is a topological space X endowed with a partial order ≤ whose graph is a closed subset of X×X. It is well-known (see, for example, [2], page 167) that if X is a regular Hausdorff space then 2X is a partially ordered space with respect to inclusion.

If ϕ(n) denotes the Euler function, for n = p a prime we have ϕ(n)/n = (1-1/p), which implies that

In this note we consider a refinement of this result. Namely, we prove that

1

where P∗(k) is the largest integer of the form where p1 < p2<…<pr are the first r primes in ascending order.