Let $s_0,s_1,s_2,\ldots$ be a sequence of rational numbers whose $m$th divided difference is integer-valued. We prove that $s_n$ polynomial function in $n$ if $s_n \ll \theta^n$ for some positive number $\theta$ satisfying $\theta < e^{1 + \tfrac{1}{2} \cdots+ \tfrac{1}{m}} -1$.

We show that for any two continuous real valued functions f, g on [0, 1], the problemZ 1

In this paper, we characterize stratifiable (or semi-stratifiable) spaces, and monotonically countably paracompact metacompact) spaces by expansions of locally upper bounded semi-continuous poset-valued maps. These extend earlier results for real-valued Locally functions.

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as fully lower semicontinuous closed convex-valued mappings that arise in variational analysis and optimization of integral functionals. The characterization allo...