Notes on the Product of Locales

Abstract

Products of locales (generalized spaces) are coproducts of frames. Because of the algebraic nature of the latter they are often viewed as algebraic objects without much topological connotation. In this paper we first analyze the frame construction emphasizing its tensor product carrier. Then we show how it can be viewed topologically, that is, in the sum-of-the-open-rectangles perspective. The main aim is to present the product from different points of view, as an algebraic and a geometric object, and persuade the reader that both of them are fairly transparent.