In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric...
28 KB (4,038 words) - 15:47, 19 June 2024
functional analysis. A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector...
103 KB (13,529 words) - 03:12, 5 July 2024
mathematics, a finite topological space is a topological space for which the underlying point set is finite. That is, it is a topological space which has only...
21 KB (2,613 words) - 18:23, 26 August 2023
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous...
14 KB (2,287 words) - 17:49, 9 September 2023
Homeomorphism (redirect from Bicontinuous topological space)
Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous...
13 KB (1,640 words) - 15:11, 11 April 2024
Topology (redirect from Topological)
invariant under such deformations is a topological property. The following are basic examples of topological properties: the dimension, which allows...
35 KB (4,041 words) - 03:13, 28 July 2024
Hausdorff space. More generally, all metric spaces are Hausdorff. In fact, many spaces of use in analysis, such as topological groups and topological manifolds...
16 KB (2,163 words) - 10:32, 20 August 2024
is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space X {\displaystyle X} is...
26 KB (3,815 words) - 01:49, 4 February 2024
and topological structures underlie the linear topological space (in other words, topological vector space) structure. A linear topological space is both...
69 KB (9,326 words) - 04:53, 24 August 2024
agree in a metric space, but may not be equivalent in other topological spaces. One such generalization is that a topological space is sequentially compact...
45 KB (5,681 words) - 09:54, 31 July 2024
Tychonoff spaces and completely regular spaces are kinds of topological spaces. These conditions are examples of separation axioms. A Tychonoff space is any...
13 KB (1,895 words) - 19:25, 20 May 2024
fundamental group of a topological space is an indicator of the failure for the space to be simply connected: a path-connected topological space is simply connected...
10 KB (1,353 words) - 16:41, 16 April 2024
and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms...
17 KB (2,428 words) - 07:40, 4 July 2024
mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space ( X , τ ) {\displaystyle (X...
6 KB (865 words) - 04:02, 21 June 2024
Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces. They are generalizations of Banach spaces (normed vector spaces that...
29 KB (5,027 words) - 09:06, 22 August 2024
In topology and related branches of mathematics, a normal space is a topological space X that satisfies Axiom T4: every two disjoint closed sets of X have...
12 KB (1,597 words) - 13:53, 8 April 2024
of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient...
18 KB (3,381 words) - 14:09, 28 April 2024
mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous...
11 KB (1,351 words) - 14:29, 4 July 2024
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence { x n } n = 1 ∞ {\displaystyle...
14 KB (2,071 words) - 12:06, 2 March 2024
In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover. The Lindelöf property is a weakening of the...
9 KB (1,180 words) - 23:26, 31 May 2024
claimed to be homeomorphic to the topological quotient. Goreham, Anthony. Sequential convergence in Topological Spaces Archived 2011-06-04 at the Wayback...
80 KB (11,075 words) - 22:00, 22 August 2024
In mathematics, a Noetherian topological space, named for Emmy Noether, is a topological space in which closed subsets satisfy the descending chain condition...
5 KB (814 words) - 03:55, 6 February 2024
authors use the term topologically complete for a wider class of topological spaces, the completely uniformizable spaces. A topological space homeomorphic to...
16 KB (2,525 words) - 07:00, 19 April 2024
Limit inferior and limit superior (redirect from Limit inferior (topological space))
motivates the definitions for general topological spaces. Take X, E and a as before, but now let X be a topological space. In this case, we replace metric...
36 KB (6,259 words) - 20:19, 12 August 2024
In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time,...
50 KB (7,492 words) - 16:51, 25 May 2024
normed vector space into a metric space and a topological vector space. If this metric space is complete then the normed space is a Banach space. Every normed...
18 KB (2,890 words) - 22:11, 21 February 2024
topology and related branches of mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair...
13 KB (1,797 words) - 02:06, 8 August 2024
Open set (section Topological space)
respectively, the topological boundary, interior, and closure of S {\displaystyle S} in X {\displaystyle X} . A topological space for which there exists...
27 KB (4,359 words) - 16:11, 15 August 2024
of mathematics, a topological manifold is a topological space that locally resembles real n-dimensional Euclidean space. Topological manifolds are an important...
17 KB (2,041 words) - 19:00, 28 June 2024
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several...
4 KB (397 words) - 00:57, 17 August 2024