mathematics, a topological algebra A {\displaystyle A} is an algebra and at the same time a topological space, where the algebraic and the topological structures...

algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are...

Topological Boolean algebra may refer to: In abstract algebra and mathematical logic, topological Boolean algebra is one of the many names that have been...

analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given...

S. (2003). "Pontryagin duality in the theory of topological vector spaces and in topological algebra". Journal of Mathematical Sciences. 113 (2): 179–349...

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants...

reflects the structure of the topological space X, the simplicial complex K, or the abelian group A. In the case of topological spaces, we arrive at the notion...

spaces, and to avoid ambiguity may also be called the algebraic dual space. When defined for a topological vector space, there is a subspace of the dual space...

In mathematics, a topological ring is a ring R {\displaystyle R} that is also a topological space such that both the addition and the multiplication are...

mathematics, a topological module is a module over a topological ring such that scalar multiplication and addition are continuous. A topological vector space...

For example, the homotopy groups of a simply connected topological space form a graded Lie algebra, using the Whitehead product. In a related construction...

usual definition goes through the notion of a σ-algebra, which is a collection of subsets of a topological space X {\displaystyle X} that contains both the...

inverse [1/x, 1/y]. Endowed with the usual topology, the algebra of intervals forms a topological ring. The group of units of this ring consists of four...

ISSN 0196-6774. Zbl 0689.68071. Hirzebruch, Friedrich (1995) [1978]. Topological methods in algebraic geometry. Classics in Mathematics. Translation from the German...

the group algebra is any of various constructions to assign to a locally compact group an operator algebra (or more generally a Banach algebra), such that...

mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory that computes topological invariants. While...

easy to describe abstractly, but in practice for C*-algebras associated to locally compact topological groups, other characterizations of the topology on...

invariant under such deformations is a topological property. The following are basic examples of topological properties: the dimension, which allows...

Common types of topological spaces include Euclidean spaces, metric spaces and manifolds. Although very general, the concept of topological spaces is fundamental...

list of topics around Boolean algebra and propositional logic. Algebra of sets Boolean algebra (structure) Boolean algebra Field of sets Logical connective...

with dimensional invariants of topological spaces. A topological algebra A over a topological field K is a topological vector space together with a continuous...

In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A...

In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time...

nonlinear algebra, while major components coming from computational mathematics support the development of the area into maturity. The topological setting...

finite-dimensional linear topological space is a homeomorphism. The three notions of dimension (one algebraic and two topological) agree for finite-dimensional...

that of a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the...

renewed in Frobenius algebras due to connections to topological quantum field theory. A finite-dimensional, unital, associative algebra A defined over a field...

Size theory Algebraic topology Topological deep learning Epstein, Charles; Carlsson, Gunnar; Edelsbrunner, Herbert (2011-12-01). "Topological data analysis"...

represented as a topological field of sets with the underlying Boolean algebra of the interior algebra corresponding to the complexes of the topological field of...

capture information about a topological or geometric space. Explicitly, a differential graded algebra is a graded associative algebra with a chain complex structure...