• topology glossary
  Topology glossary
  This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology...
  
  
• List of general topology topics
• List of geometric topology topics
• List of algebraic topology topics
• List of topological invariants (topological properties)
  Topological property
  In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms. That is, a property of spaces is a topological property if whenever a space X possesses that property every space homeomorphic...
  
  
• Publications in topology

Topology and physics

• Quantum topology
  Quantum topology
  Quantum topology is a branch of mathematics that connects quantum mechanics with low-dimensional topology.Dirac notation provides a viewpoint of quantum mechanics which becomes amplified into a framework that can embrace the amplitudes associated with topological spaces and the related embedding of...
  
  
• Topological defect
  Topological defect
  In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution; it can be proven to exist because the boundary conditions entail the existence of...
  
  
• Topological entropy in physics
• Topological order
  Topological order
  In physics, topological order is a new kind of order in a quantum state that is beyond the Landau symmetry-breaking description. It cannot be described by local order parameters and long range correlations...
  
  
• Topological quantum field theory
  Topological quantum field theory
  A topological quantum field theory is a quantum field theory which computes topological invariants....
  
  
• Topological quantum number
  Topological quantum number
  In physics, a topological quantum number is any quantity, in a physical theory, that takes on only one of a discrete set of values, due to topological considerations...
  
  
• Topological string theory
  Topological string theory
  In theoretical physics, topological string theory is a simplified version of string theory. The operators in topological string theory represent the algebra of operators in the full string theory that preserve a certain amount of supersymmetry...
  
  
• Topology of the universe

Topology and dynamical systems

• Milnor–Thurston kneading theory
  Milnor–Thurston kneading theory
  The Milnor–Thurston kneading theory is a mathematical theory which analyzes the iterates of piecewise monotone mappings of an interval into itself...
  
  
• Topological conjugacy
• Topological dynamics
  Topological dynamics
  In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.- Scope :...
  
  
• Topological entropy
  Topological entropy
  In mathematics, the topological entropy of a topological dynamical system is a nonnegative real number that measures the complexity of the system. Topological entropy was first introduced in 1965 by Adler, Konheim and McAndrew. Their definition was modelled after the definition of the...
  
  
• Topological mixing

Topology and computing

• Computational topology
• Digital topology
  Digital topology
  Digital topology deals with properties and features of two-dimensional or three-dimensional digital imagesthat correspond to topological properties or topological features of objects....
  
  
• Network topology
  Network topology
  Network topology is the layout pattern of interconnections of the various elements of a computer or biological network....
  
  
• Topological computing
  Topological computing
  Topological computing is the designing and building of hardware and software based on the processing of topologically modulated electromagnetic impulses that differ from each other in their spatio-temporal topology.-Science and theory:...
  
  
• Topological Quantum Computing
• Topological quantum computer
  Topological quantum computer
  A topological quantum computer is a theoretical quantum computer that employs two-dimensional quasiparticles called anyons, whose world lines cross over one another to form braids in a three-dimensional spacetime . These braids form the logic gates that make up the computer...
  
  

Miscellaneous

• Combinatorial topology
  Combinatorial topology
  In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces were regarded as derived from combinatorial decompositions such as simplicial complexes...
  
  
• Counterexamples in Topology
  Counterexamples in Topology
  Counterexamples in Topology is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr.In the process of working on problems like the metrization problem, topologists have defined a wide variety of topological properties...
  
  
• Differential topology
  Differential topology
  In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.- Description :...
  
  
• Geometric topology
  Geometric topology
  In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
  
  
• Geospatial topology
  Geospatial topology
  Geospatial topology studies the rules concerning the relationships between the points, lines, and polygons that represent the features of a geographic region. For example, where two polygons represent adjacent counties, typical topological rules would require that the counties share a common...
  
  
• Grothendieck topology
  Grothendieck topology
  In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a site.Grothendieck topologies axiomatize the notion...
  
  
• Link topology
  Link topology
  Link topology is the study of the linked structure of the World Wide Web.See also: Link awareness...
  
  
• Listing number
• Mereotopology
  Mereotopology
  In formal ontology, a branch of metaphysics, and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts....
  
  
• Noncommutative topology
  Noncommutative topology
  Noncommutative topology in mathematics is a term applied to the strictly C*-algebraic part of the noncommutative geometry program. The program has its origins in the Gel'fand duality between the topology of locally compact spaces and the algebraic structure of commutative C*-algebras.Several...
  
  
• Pointless topology
  Pointless topology
  In mathematics, pointless topology is an approach to topology that avoids mentioning points. The name 'pointless topology' is due to John von Neumann...
  
  
• Set-theoretic topology
  Set-theoretic topology
  In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independent of ZFC. A famous problem is the normal Moore space question, a question in general topology that was the subject of intense research. The...
  
   
• Topological combinatorics
  Topological combinatorics
  The discipline of combinatorial topology used combinatorial concepts in topology and in the early 20th century this gradually turned into the field of algebraic topology....
  
  
• Topological data analysis
  Topological data analysis
  Topological data analysis is a new area of study aimed at having applications in areas such as data mining and computer vision.The main problems are:# how one infers high-dimensional structure from low-dimensional representations; and...
  
  
• Topological degree theory
  Topological degree theory
  In mathematics, topological degree theory is a generalization of the winding number of a curve in the complex plane. It can be used to estimate the number of solutions of an equation, and is closely connected to fixed-point theory. When one solution of an equation is easily found, degree theory can...
  
  
• Topological game
  Topological game
  A topological game is an infinite positional game of perfect information played between two players on a topological space. Players choose objects with topological properties such as points, open sets, closed sets and open coverings. Time is generally discrete, but the plays may have transfinite...
  
  
• Topological graph theory
  Topological graph theory
  In mathematics topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces. It also studies immersions of graphs....
  
  
• Topological K-theory
  Topological K-theory
  In mathematics, topological K-theory is a branch of algebraic topology. It was founded to study vector bundles on general topological spaces, by means of ideas now recognised as K-theory that were introduced by Alexander Grothendieck...
  
  
• Topological modular forms
  Topological modular forms
  In mathematics, the spectrum of topological modular forms describes a generalized cohomology theory whose coefficient ring is related to the graded ring of holomorphic modular forms with integral cusp expansions...
  
  
• Topological skeleton
  Topological skeleton
  In shape analysis, skeleton of a shape is a thin version of that shape that is equidistant to its boundaries. The skeleton usually emphasizes geometrical and topological properties of the shape, such as its connectivity, topology, length, direction, and width...
  
  
• Topology optimization
  Topology optimization
  - Introduction :Topology optimisation is a mathematical approach that optimises material layout within a given design space, for a given set of loads and boundary conditions such that the resulting layout meets a prescribed set of performance targets...
  
  
• Water, gas, and electricity