Topological abelian group information

mathematics, a topological abelian group, or TAG, is a topological group that is also an abelian group. That is, a TAG is both a group and a topological space...

example, in physics. In functional analysis, every topological vector space is an additive topological group with the additional property that scalar multiplication...

A topological group is a locally compact group if the underlying topological space is locally compact and Hausdorff; a topological group is abelian if...

Ordered topological vector space Topological abelian group – concept in mathematicsPages displaying wikidata descriptions as a fallback Topological field –...

special case of the types preceding it: sets, topological spaces, uniform spaces, TAGs (topological abelian groups), normed spaces, Euclidean spaces, and the...

{\displaystyle X} and G {\displaystyle G} are topological abelian groups. A topological abelian group G {\displaystyle G} belongs to the class S ( T...

abelian groups. A topological group is called locally compact if the underlying topological space is locally compact and Hausdorff; the topological group...

mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does...

"Creation of Non-Abelian Topological Order and Anyons on a Trapped-Ion Processors". arXiv:2305.03766 [quant-ph]. Non-Abelian topological order (TO) is a...

an example, the direct sum of two abelian groups A {\displaystyle A} and B {\displaystyle B} is another abelian group A ⊕ B {\displaystyle A\oplus B} consisting...

In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same...

In mathematics, a topological group G is called a discrete group if there is no limit point in it (i.e., for each element in G, there is a neighborhood...

In geometry, an abelian Lie group is a Lie group that is an abelian group. A connected abelian real Lie group is isomorphic to R k × ( S 1 ) h {\displaystyle...

In mathematics, a free abelian group is an abelian group with a basis. Being an abelian group means that it is a set with an addition operation that is...

notion is a free abelian group; both notions are particular instances of a free object from universal algebra. As such, free groups are defined by their...

the classification of abelian groups: according to the fundamental theorem of finite abelian groups, every finite abelian group can be expressed as the...

abelian groups, are much better behaved than the category of topological spaces. In particular, unlike the category of topological abelian groups, the category...

Various topologically ordered states have interesting properties, such as (1) topological degeneracy and fractional statistics or Non-abelian Group statistics...

redirect targets Topological abelian group – concept in mathematicsPages displaying wikidata descriptions as a fallback Topological field – Algebraic...

functions on abelian groups. Similarly to how exponential functions on exponential fields are defined, given a topological abelian group G a homomorphism...

isomorphic to the additive group of Z/nZ, the integers modulo n. Every cyclic group is an abelian group (meaning that its group operation is commutative)...

cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology...

realization of non-abelian anyons on quantum processors, the first used a toric code with twist defects as a topological degenerancy (or topological defect) while...

mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops...