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...

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...

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

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...

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

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...

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...

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

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...

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

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...

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

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

in A, and the quotient is given the quotient topology. As a set, X ∪f Y consists of the disjoint union of X and (Y − A). The topology, however, is specified...

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

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...

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...

induces the quotient topology on X / C . {\displaystyle X/C.} If X {\displaystyle X} is a Hausdorff locally convex topological vector space then the following...

trivial topology is its poor separation properties: its Kolmogorov quotient is the one-point space. A first-countable, separable Hausdorff space (in particular...

In topology and related branches of mathematics, a totally disconnected space is a topological space that has only singletons as connected subsets. In...

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

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

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

construction quotient Topological tensor product Discrete space Locally constant function Trivial topology Cofinite topology Finer topology Product topology Restricted...

In topology, a topological space X {\displaystyle X} is called a compactly generated space or k-space if its topology is determined by compact spaces in...

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

In topology and related fields of mathematics, a topological space X is called a regular space if every closed subset C of X and a point p not contained...

syntax-semantics interface formalism based on linear logic Quotient space (topology), or gluing spaces, the concept of gluing points or subspaces together Glu...

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