Note that the P produced in Theorem 2 need not have dP=0.
......where the Pk are polynomials.
We characterize the Banach spaces X for which n(X)=1.
Thus πn(X) can be interpreted as the homotopy classes of maps Sn→ X. [= as the set of all homotopy classes]
It has some basic properties in common with another most important class of functions, namely, the continuous ones.
In the plane, the open sets are those which are unions of open circular discs.
the number of zeros of f in D
the density of the zeros of f
Let A be the union of the sets f(Q) for f in F.
Here p2(r) is the sum of the squares of the divisors of r.
The problem has a very natural connection with the problem of the distribution of the zeros of a bounded holomorphic function in a half-plane.
Intuitively, entropy of a partition is a measure of its information content---the larger the entropy, the larger the information content.