"In mathematics, topology is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself."
The study of the properties of spaces that are preserved under continuous transformations, including the study of manifolds (higher dimensional spaces).
"A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity."
"Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology."
"The deformations that are considered in topology are homeomorphisms and homotopies."
"A property that is invariant under such deformations is a topological property. The following are basic examples of topological properties: the dimension... compactness... connectedness..."
"The ideas underlying topology go back to Gottfried Leibniz, who in the 17th century envisioned the geometria situs and analysis situs."
"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."
"It was not until the first decades of the 20th century that the idea of a topological space was developed."
"The word 'topology' comes from the Greek words τόπος, 'place, location', and λόγος, 'study'."
"A topological space is a set endowed with a structure, called a topology..."
"...allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity."
"The dimension, which allows distinguishing between a line and a surface..."
"Euclidean spaces, and, more generally, metric spaces are examples of a topological space..."
"The deformations that are considered in topology are homeomorphisms and homotopies."
"A property that is invariant under such deformations is a topological property."
"The term topology was introduced by Johann Benedict Listing..."
"Leonhard Euler's Seven Bridges of Königsberg problem and polyhedron formula are arguably the field's first theorems."
"It was not until the first decades of the 20th century that the idea of a topological space was developed."
"...that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself."