
related topics 
{math, number, function} 
{@card@, make, design} 
{theory, work, human} 
{food, make, wine} 
{line, north, south} 
{work, book, publish} 
{island, water, area} 
{town, population, incorporate} 

Topology (from the Greek τόπος, “place”, and λόγος, “study”) is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example, deformations that involve stretching, but no tearing or gluing. It emerged through the development of concepts from geometry and set theory, such as space, dimension, and transformation.
Ideas that are now classified as topological were expressed as early as 1736. Toward the end of the 19th century, a distinct discipline developed, which was referred to in Latin as the geometria situs (“geometry of place”) or analysis situs (GreekLatin for “picking apart of place”). This later acquired the modern name of topology. By the middle of the 20^{th} century, topology had become an important area of study within mathematics.
The word topology is used both for the mathematical discipline and for a family of sets with certain properties that are used to define a topological space, a basic object of topology. Of particular importance are homeomorphisms, which can be defined as continuous functions with a continuous inverse. For instance, the function y = x^{3} is a homeomorphism of the real line.
Topology includes many subfields. The most basic and traditional division within topology is pointset topology, which establishes the foundational aspects of topology and investigates concepts inherent to topological spaces (basic examples include compactness and connectedness); algebraic topology, which generally tries to measure degrees of connectivity using algebraic constructs such as homotopy groups and homology; and geometric topology, which primarily studies manifolds and their embeddings (placements) in other manifolds. Some of the most active areas, such as low dimensional topology and graph theory, do not fit neatly in this division.
See also: topology glossary for definitions of some of the terms used in topology and topological space for a more technical treatment of the subject.
Contents
Full article ▸


related documents 
Integer factorization 
Expander graph 
LL parser 
Algebraically closed field 
Stokes' theorem 
Even and odd permutations 
Associative array 
Document Type Definition 
Cauchy's integral formula 
Line integral 
Parameter 
Morphism 
Optimization (mathematics) 
Yoneda lemma 
Stone–Weierstrass theorem 
Henri Lebesgue 
Positivedefinite matrix 
Boolean algebra (structure) 
Finite difference 
Banach space 
Solvable group 
Hypercomplex number 
Universal quantification 
Liouville number 
Bspline 
A* search algorithm 
Haskell (programming language) 
Topological vector space 
Free group 
Geometric series 
