Topology is a branch of mathematics, 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 on set theory, considering both sets of points and families of sets.
The word topology is used both for the area of study, and for a family of sets with certain properties described below.
Of particular importance in the study of topology are functions or maps that are continuous.
These functions stretch space without tearing it apart or sticking distinct parts together.