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... 11 KB (1,544 words) - 00:20, 22 February 2024 |
as spaces. In particular: Quotient space (topology), in case of topological spaces Quotient space (linear algebra), in case of vector spaces Quotient space... 399 bytes (88 words) - 02:08, 18 October 2020 |
In topology and related branches of mathematics, a Hausdorff space (/ˈhaʊsdɔːrf/ HOWSS-dorf, /ˈhaʊzdɔːrf/ HOWZ-dorf), separated space or T2 space is a... 16 KB (2,177 words) - 11:54, 28 February 2024 |
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... 12 KB (2,191 words) - 01:48, 26 September 2023 |
Quotient object Quotient of a formal language, also left and right quotient Quotient ring Quotient set Quotient space (topology) Quotient type Quotition... 8 KB (825 words) - 17:38, 25 February 2024 |
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... 13 KB (1,797 words) - 20:06, 26 April 2024 |
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... 28 KB (4,040 words) - 06:46, 8 April 2024 |
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... 12 KB (1,922 words) - 06:22, 22 December 2023 |
In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base. More explicitly... 5 KB (726 words) - 19:57, 24 November 2023 |
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... 4 KB (540 words) - 01:53, 17 April 2024 |
Equivalence class (redirect from Quotient set) quotient spaces in linear algebra, quotient spaces in topology, quotient groups, homogeneous spaces, quotient rings, quotient monoids, and quotient categories... 16 KB (2,323 words) - 22:11, 30 January 2024 |
topology) is sometimes used as a synonym, especially in functional analysis. When a topology is generated using a family of pseudometrics, the space is... 8 KB (1,273 words) - 17:50, 27 December 2023 |
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... 42 KB (5,724 words) - 02:31, 8 November 2023 |
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... 103 KB (13,527 words) - 23:11, 26 April 2024 |
an equivalence relation Quotient group Quotient ring Quotient module Quotient space (linear algebra) Quotient space (topology), by an equivalence relation... 896 bytes (142 words) - 08:54, 8 May 2023 |
In topology and related branches of mathematics, a totally disconnected space is a topological space that has only singletons as connected subsets. In... 6 KB (880 words) - 15:18, 17 April 2024 |
In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies... 37 KB (6,872 words) - 03:09, 29 April 2024 |
trivial topology is its poor separation properties: its Kolmogorov quotient is the one-point space. A first-countable, separable Hausdorff space (in particular... 14 KB (2,071 words) - 12:06, 2 March 2024 |
hyperconnected space is connected. Identification map See Quotient map. Identification space See Quotient space. Indiscrete space See Trivial topology. Infinite-dimensional... 55 KB (7,583 words) - 12:00, 19 April 2024 |
construction quotient Topological tensor product Discrete space Locally constant function Trivial topology Cofinite topology Finer topology Product topology Restricted... 5 KB (393 words) - 12:17, 30 October 2023 |
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... 30 KB (4,652 words) - 04:03, 14 October 2023 |
In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks... 19 KB (2,532 words) - 15:27, 24 December 2023 |
induced topology. Every normed space is automatically assumed to carry this Hausdorff topology, unless indicated otherwise. With this topology, every Banach... 103 KB (17,214 words) - 08:06, 6 March 2024 |
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... 9 KB (1,128 words) - 18:26, 9 February 2024 |
the subspace topology (or the relative topology, or the induced topology, or the trace topology).[citation needed] Given a topological space ( X , τ ) {\displaystyle... 8 KB (1,379 words) - 21:27, 24 April 2024 |