topology

Introduction

CE5

Möbius strip: On the ordinary flat loop (A), an ant walking along the middle of the strip will pass only around the outside of the strip. If the strip is cut along the dotted line, twisted once, and rejoined to form the Möbius strip (B), a different topological space results; the ant walking along the middle of the strip will pass around both inside and outside.

topology, branch of mathematics, formerly known as analysis situs, that studies patterns of geometric figures involving position and relative position without regard to size. Topology is sometimes referred to popularly as “rubber-sheet geometry” because a figure can be changed to that of an equivalent figure by bending, stretching, twisting, and the like, but not by tearing or cutting.

Sections in this article:

Introduction
Topological Properties
Continuous Transformations and Equivalent Figures
Branches of Topology

See more Encyclopedia articles on: Mathematics