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

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...

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...

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

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

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

In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets...

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...

particularly in the field of topology, the K-topology, also called Smirnov's deleted sequence topology, is a topology on the set R of real numbers which...

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

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

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

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...

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

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

its elements is an open set. Covers are commonly used in the context of topology. If the set X {\displaystyle X} is a topological space, then a cover C...

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...

mathematics, pointless topology, also called point-free topology (or pointfree topology) and locale theory, is an approach to topology that avoids mentioning...

areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric...

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 ,...

can be open (the discrete topology), or no subset can be open except the space itself and the empty set (the indiscrete topology). In practice, however,...

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...

In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed...

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

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...

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

In general topology and related areas of mathematics, the final topology (or coinduced, weak, colimit, or inductive topology) on a set X , {\displaystyle...

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