Generalizing shapes

We now consider the simplest structure in the preceding figure, the topological space. As is often done, if there is no risk of confusion we will shorten this to just “space.” Spaces essentially only include the intuitive idea of “shape”; the higher structures and ideas present in manifolds and beyond will be considered in separate chapters.

 ◊ A good picture to keep in mind for a space is a rubber sheet that can be stretched or shrunk, but cannot be torn or glued.