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 (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...

Men of New York! Why are you no longer throwing your scarves carelessly, rakishly over your shoulders, ends trailing in the wind? Why are you now pausing to double those scarves, holding the looped end at one side of your necks, then drawing the ends...

It pays to be curious, to ask questions and seek answers.That's what Mary Masterman found out. From a very young age, Masterman, now 18, asked thought-provoking questions.When she was in the eighth grade, her father gave her a telescope. When she looked at stars and...