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...

as spaces. In particular: Quotient space (topology), in case of topological spaces Quotient space (linear algebra), in case of vector spaces Quotient space...

In topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology...

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

In linear algebra, the quotient of a vector space V {\displaystyle V} by a subspace N {\displaystyle N} is a vector space obtained by "collapsing" N {\displaystyle...

Quotient object Quotient of a formal language, also left and right quotient Quotient ring Quotient set Quotient space (topology) Quotient type Quotition...

quotient spaces in linear algebra, quotient spaces in topology, quotient groups, homogeneous spaces, quotient rings, quotient monoids, and quotient categories...

specifically, a topological space is a set whose elements are called points, along with an additional structure called a topology, which can be defined as...

In topology and related branches of mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every...

\delta ).} The quotient metric does not always induce the quotient topology. For example, the topological quotient of the metric space N × [ 0 , 1 ] {\displaystyle...

In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base. More explicitly...

In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies...

In mathematics, an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another...

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

disconnected subspaces of R² In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the...

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

In topology and related branches of mathematics, a T1 space is a topological space in which, for every pair of distinct points, each has a neighborhood...

topological spaces into X , {\displaystyle X,} is the finest topology on X {\displaystyle X} that makes all those functions continuous. The quotient topology on...

pointed space Y {\displaystyle Y} with basepoint y 0 {\displaystyle y_{0}} is a based map if it is continuous with respect to the topologies of X {\displaystyle...

vector space. Given a subspace M ⊆ X , {\displaystyle M\subseteq X,} the quotient space X / M {\displaystyle X/M} with the usual quotient topology is a...

topology) is sometimes used as a synonym, especially in functional analysis. When a topology is generated using a family of pseudometrics, the space is...

coimage of f , {\displaystyle f,} if given the quotient space topology, must also be a Hausdorff space. A space is compact if and only if the kernel of every...

induced topology. Every normed space is automatically assumed to carry this Hausdorff topology, unless indicated otherwise. With this topology, every Banach...

an equivalence relation Quotient group Quotient ring Quotient module Quotient space (linear algebra) Quotient space (topology), by an equivalence relation...

hyperconnected space is connected. Identification map See Quotient map. Identification space See Quotient space. Indiscrete space See Trivial topology. Infinite-dimensional...

In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks...

topology on Y for which f is continuous. A common example of a quotient topology is when an equivalence relation is defined on the topological space X...

called the subspace topology (or the relative topology, or the induced topology, or the trace topology). Given a topological space ( X , τ ) {\displaystyle...

it with "at least one" is equivalent to the property that the T0 quotient of the space is sober, which is sometimes referred to as having "enough points"...

In topology, a branch of mathematics, a graph is a topological space which arises from a usual graph G = ( E , V ) {\displaystyle G=(E,V)} by replacing...