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Topology 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 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 that are used to define a topological space. Of particular importance in the study of topology are functions or maps that are homeomorphisms. Informally, these functions can be thought of as those that stretch space without tearing it apart or sticking distinct parts together.