Time: 9h00, Wednesday, December 5, 2018
Location: Rom 302, Building A5, Institute of Mathematics
Abstract: While a product of continuous real-valued functions defined on a metric space must be continuous, the product of a pair of uniformly continuous real functions need not be, even if one is bounded. We give necessary and sufficient conditions for (i) the product of a pair of such functions to be uniformly continuous, and for (ii) the product of an arbitrary pair of such functions to be uniformly continuous, that is, for the vector space of real uniformly continuous functions to form a ring. It is amazing that neither of these basic questions had been resolved until recently.