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 α4 Fréchet spaces (also known as strongly Fréchet or countably bisequential spaces) is α4, 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 α3 Fréchet spaces and its subclass of ℵ0-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 α3 and Fréchet and being ℵ0-bisequential.