what is topology?

Answer 1

Topology (Greek topos, place and logos, study) is a branch of mathematics, which 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. 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.

When the discipline was first properly founded, toward the end of the 19th century, it was called geometria situs (Latin geometry of place) and analysis situs (Latin analysis of place). From around 1925 to 1975 it was a most important growth area within mathematics.

Topology is a large branch of mathematics which includes many subfields. The most basic division within topology is into point-set topology, which investigates such concepts as compactness, connectedness, and countability, and algebraic topology, which investigates such concepts as homotopy, homology, and knot theory.

Answer 2

http://dictionary.reference.com/browse/topology

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