Continuity is conventionally associated with functions defined on the real line or higher-dimensional Euclidean spaces. Topology is concerned with the abstraction of continuity to maps between more general sets. The subject is vast and its study can...

Mathematics began in earliest times as a collection of practical methods for counting and measuring. In the nineteenth century a branch of geometry arose in which sizes and distances were irrelevant. Topology, sometimes called "rubber sheet...

Topology is the study of properties of objects that do not depend on geometric measurements, and that do not change when the object is stretched or distorted without tearing. Topology is divided into three subdisciplines, which are largely different...

The ancient Prussian city of Königsberg contained seven bridges. According to a tradition among the residents of Königsberg, it was impossible to walk over all seven bridges without crossing one of them at least twice. That problem came to...

Topology is sometimes called "rubber-sheet geometry" because if a shape is drawn on a rubber sheet (like a piece of a balloon), then all of the shapes you can make by stretching or twisting—but never tearing—the sheet are...

Topology is the study of the properties of spaces that are insensitive to continuous deformations. Physicists recognize several different subdivisions of topology. The simplest is called point set topology, which is needed to define the notion of a...

(from Greek, topos, a place, and logos, discourse) Topology is the study of the relationships between places. (More specifically, in mathematics, topology is the systematic study of connected or adjacent points of a plane or space which remain present...

1 word order 2 Spatial relations between objects whose specification is necessary for descriptions of space (especially for the use of prepositions). Such topological concepts (which are probably universal) include inner (in, inside of) vs outer...

In mathematics, the study of the properties of a geometric object that remains unchanged by deformations such as bending, stretching, or squeezing but not breaking. A sphere is topologically equivalent to a cube because, without breaking them, each can...

A term referring to the physical connection method used to connect computers on a...

Topology (Greek topos, "place," and logos, "study") is a branch of mathematics that is an extension of geometry. Topology begins with a consideration of the nature of space, investigating both its fine structure and its global structure. Topology builds...