Paracompactness, normality, and related properties of topologies on infinite products

摘要

There are a number of ways to create products of spaces, where we say that a topology on Pi(i)is an element of I/X-i is a product (as opposed to the product) topology if each projection of an open set is open. The smallest such product topology is the Tychonoff product (a.k.a. the product): a basic set restricts on finitely many coordinates. The largest such product topology is the box product: a basic set restricts independently on each coordinate. In this paper we will focus on the box product (which Mary Ellen Rudin worked on and proselytized about), and on the uniform box product (a naturally defined intermediate product between the Tychonoff product and the box product).