In topology, a branch of mathematics, an extension topology is a topology placed on the disjoint union of a topological space and another set. There are...

Closed extension topology Finite excluded point topology Countable excluded point topology Uncountable excluded point topology Open extension topology Either-or...

The cocountable topology, also known as the countable complement topology, is a topology that can be defined on any infinite set X {\displaystyle X} ....

, {\displaystyle (X,\tau ),} the cocountable extension topology on X {\displaystyle X} is the topology having as a subbasis the union of τ and the family...

In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such...

particular point topology is the closed extension topology. In the case when X \ {p} has the discrete topology, the closed extension topology is the same as...

In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem or Urysohn-Brouwer lemma) states that any real-valued...

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

differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct...

point topology If X is uncountable, the topology on X is called the uncountable excluded point topology A generalization is the open extension topology; if...

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...

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

extension property, in topology Kolmogorov extension theorem, in probability theory Linear extension, in order theory Sheaf extension, in algebraic geometry...

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

of triangulations established a new branch in topology, namely piecewise linear topology (or PL topology). Its main purpose is to study the topological...

In topology and related branches of mathematics, a Hausdorff space (/ˈhaʊsdɔːrf/ HOWSS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf), T2 space or separated space, is a...

extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension....

Tree Protocol (STP) is a network protocol that builds a loop-free logical topology for Ethernet networks. The basic function of STP is to prevent bridge loops...

In general topology, an Alexandrov topology is a topology in which the intersection of an arbitrary family of open sets is open (while the definition of...

In topology, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace....

In mathematics, in the area of algebraic topology, the homotopy extension property indicates which homotopies defined on a subspace can be extended to...

Dugundji extension theorem - a theorem in topology, named after the American mathematician James Dugundji Extension Lemma - a lemma in topology (resp. functional...

cocountable extension topology is the topology on the real line generated by the union of the usual Euclidean topology and the cocountable topology. Sets are...

In topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else...

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean...

This is a list of algebraic topology topics. Simplex Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem...

A notable offspring of GeoJSON is TopoJSON, an extension of GeoJSON that encodes geospatial topology and that typically provides smaller file sizes....

NeuroEvolution of Augmenting Topologies (NEAT) is a genetic algorithm (GA) for generating evolving artificial neural networks (a neuroevolution technique)...

In topology, two continuous functions from one topological space to another are called homotopic (from Ancient Greek: ὁμός homós 'same, similar' and τόπος...