Abstract

Topology is a kind of abstraction from metrical geometry. The metrical geometry is the distance geometry of a space and gives rise to concepts such as length, angles, and curvature. Topology studies spaces with a much more general conception of “nearness” than that provided by the metric. Thus, although the metric geometry distinguishes spheres, cubes, and pyramids from one another due to their different metrical properties, topology classifies them together as instances of the same object. However, topology does mark a difference between spheres and doughnuts since, loosely speaking, “holes” are topological properties. Explaining the difference between topological and metrical properties is therefore the natural first order of business when introducing the ideas of topology.