H-Spaces and Co-H-Spaces

Abstract

From this chapter on, most of the spaces that we consider will be based and path-connected and have the based homotopy type of based CW complexes. Some notable exceptions to path-connectedness are the 0-sphere S ⁰ and the 0-skeleton of a CW complex. Unless otherwise stated, all functions under con- sideration will be continuous and based and all homotopies will preserve the base point. These restrictions are sometimes asserted explicitly for empha- sis. We discuss unbased spaces, functions and homotopies from time to time. However, whenever doing so, we explicitly make note of the fact.