## ::Topology

### ::concepts

Topology::topology    Space::theory    Called::function    Spaces::first    Geometry::homotopy    Title::which

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Möbius strips, which have only one surface and one edge, are a kind of object studied in topology.

In mathematics, topology (from the Greek τόπος, place, and λόγος, study), is the study of a collection of open sets, making a given set a topological space. It is an area of mathematics concerned with the properties of space that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing. Important topological properties include connectedness and compactness.<ref>http://dictionary.reference.com/browse/topology</ref>

Topology developed as a field of study out of geometry and set theory, through analysis of such concepts as space, dimension, and transformation.<ref>http://www.math.wayne.edu/~rrb/topology.html</ref> Such ideas go back to Gottfried Leibniz, who in the 17th century envisioned the geometria situs (Greek-Latin for "geometry of place") and analysis situs (Greek-Latin for "picking apart of place"). Leonhard Euler's Seven Bridges of Königsberg Problem and Polyhedron Formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. By the middle of the 20th century, topology had become a major branch of mathematics.

Topology has many subfields:

A three-dimensional depiction of a thickened trefoil knot, the simplest non-trivial knot

Topology sections