Workshop lecture on products of Fréchet spaces

The general question, “When is the product of Fréchet spaces Fréchet?” really depends on the questions of when a product of α 4 Fréchet spaces (also known as strongly Fréchet or countably bisequential spaces) is α 4 , and when it is Fréchet. Two subclasses of the class of strongly Fréchet spaces shed much light on these questions. These are the class of α 3 Fréchet spaces and its subclass of ℵ 0 -bisequential spaces. The latter is closed under countable products, the former not even under finite products. A number of fundamental results and open problems are recalled, some further highlighting the difference between being α 3 and Fréchet and being ℵ 0 -bisequential.