topology

The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).

1970 [Addison-Wesley], Stephen Willard, General Topology, 2012, Dover, page v, This book is designed to develop the fundamental concepts of general topology which are the basic tools of working mathematicians in a variety of fields.

1974 [Crane, Russak & Co.], H. Graham Flegg, From Geometry to Topology, 2001, Dover, page v, Many university courses in topology plunge immediately into a formalized and entirely abstract presentation of topological concepts.

Any collection τ of subsets of a given set X that contains both the empty set and X, and which is closed under finitary intersections and arbitrary unions.

A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau).

The subsets of a set X which constitute a topology are called the open sets of X.

The anatomical structure of part of the body.

The arrangement of nodes in a communications network.

The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.