Examples of 'topological group' in a sentence
Meaning of "topological group"
Topological group: In mathematics, a topological group is a group G together with a topology on G such that the group's binary operation and the group's inverse function are continuous functions
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- A group which is also a topological space and whose group operations are continuous functions.
How to use "topological group" in a sentence
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topological group
Every topological group is completely regular.
Locally compact topological group.
Every topological group is homogeneous.
This need not be true in a general abelian topological group see examples below.
A topological group is a topological semigroup.
This much is a fragment of a typical locally Euclidean topological group.
A topological group is a group object in the category of topological spaces with continuous functions.
The Bredon cohomology of topological spaces under action of a topological group is named after him.
A topological group is a mathematical object with both an algebraic structure and a topological structure.
The inversion operation on a topological group G is a homeomorphism from G to itself.
Every locally compact group which is second-countable is metrizable as a topological group i . e.
A discrete group is a topological group G equipped with the discrete topology.
Thus, the idele group is a topological group.
A discrete subgroup of a topological group G is a subgroup H whose relative topology is the discrete one.
Therefore, the group of units is not a topological group in general.
See also
Is every topological group the topological fundamental group of an space?
More generally, every commutative topological group is also a uniform space.
For most practical purposes continuous symmetry is modelled by a "group action" of a topological group.
In mathematics, a totally disconnected group is a topological group that is totally disconnected.
For example, a topological group is just a group in the category of topological spaces.
A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group.
Indeed, any non-discrete topological group is also a topological group when considered with the discrete topology.
In an SMP system, a node can be defined as a topological group of agents / processors.
A topological group is Hausdorff if and only if the trivial one-element subgroup is closed.
Its algebraic structure and topology make it into a Lie group, a type of topological group.
Equivalently, a locally profinite group is a topological group that is Hausdorff locally compact and totally disconnected.
Since the transformations depend continuously on s, v, R, a, Gal ( 3 ) is a continuous group, also called a topological group.
Specifically, let G be a topological group which acts continuously on the fiber space F on the left.
The real numbers, R with the usual topology form a topological group under addition.
For example, in any topological group the identity component i . e.
With this topology, G becomes a topological group.
In mathematics, a compact ( topological ) group is a topological group whose topology is compact.
In mathematics, a compact ( topological, often understood ) group is a topological group whose topology is compact.
The topology associated to a filtration on a group G { \ displaystyle G } makes G { \ displaystyle G } into a topological group.
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Examples of using Group
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Salbutamol is one of a group of medicines called bronchodilators
No group of people is more or less deserving of protection
Donor support working group meetings were held
Examples of using Topological
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An orbispace is to topological spaces what an orbifold is to manifolds
Interconnection networks and their topological properties
Topological defects in nematic droplets of hard spherocylinders
