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...

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

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 topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every...

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...

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...

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

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

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

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

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...

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...

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

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...

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

topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology. Roughly...

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

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...

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

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, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space. Such spaces are commonly...

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

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...

In topology, an Alexandrov topology is a topology in which the intersection of every family of open sets is open. It is an axiom of topology that the...

sequences form sequence spaces, respectively denoted c and c0, with the sup norm. Any sequence space can also be equipped with the topology of pointwise convergence...

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