Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the part of mathematics concerned with the properties of a geometric object...

Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe...

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants...

In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators,...

elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy...

In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set. This order relation can...

coarsest topology may refer to: Initial topology, the most coarse topology in a certain category of topologies Trivial topology, the most coarse topology possible...

natural topology called the product topology. This topology differs from another, perhaps more natural-seeming, topology called the box topology, which...

Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation...

from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology). Given a topological space ( X ,...

The cocountable topology or countable complement topology on any set X consists of the empty set and all cocountable subsets of X, that is all sets whose...

Look up topology in Wiktionary, the free dictionary. Topology is a branch of mathematics concerned with geometric properties preserved under continuous...

general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It...

mathematics, an order topology is a specific topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real...

general topology and related areas of mathematics, the initial topology (or induced topology or weak topology or limit topology or projective topology) on...

and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves...

In martingale theory, Émery topology is a topology on the space of semimartingales. The topology is used in financial mathematics. The class of stochastic...

topology τ of a topological space (X, τ) is a family B {\displaystyle {\mathcal {B}}} of open subsets of X such that every open set of the topology is...

Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads, boundary conditions...

In mathematics, particularly topology, the K-topology is a topology that one can impose on the set of all real numbers which has some interesting properties...

primarily by its curvature, while the global geometry is characterised by its topology (which itself is constrained by curvature). General relativity explains...

a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different topologies depending on...

Electronic filter topology defines electronic filter circuits without taking note of the values of the components used but only the manner in which those...

In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on n {\displaystyle n} -dimensional Euclidean space...

algebra, the Zariski topology is a topology defined on geometric objects called varieties. It is very different from topologies that are commonly used...

plasma physics, the magnetic topology of a plasma is the structure and linkage of its magnetic field. The magnetic topology of a plasma can be changed through...

topology, the cartesian product of topological spaces can be given several different topologies. One of the more natural choices is the box topology,...

mathematical field of functional analysis there are several standard topologies which are given to the algebra B(X) of bounded linear operators on a Banach...

most general continuous functions, and their definition is the basis of topology. A stronger form of continuity is uniform continuity. In order theory,...

uniform topology on a space may mean: In functional analysis, it sometimes refers to a polar topology on a topological vector space. In general topology, it...