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...

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

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...

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

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...

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...

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

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...

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...

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...

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

For a topological space X, the collection of all Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X...

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

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

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

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

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...

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

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

This is a list of general topology topics. Topological space Topological property Open set, closed set Clopen set Closure (topology) Boundary (topology)...

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

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

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

Another refinement of the notion of a field is a topological field, in which the set F is a topological space, such that all operations of the field (addition...

sense, with the algebraic structure. Topological group: a group with a topology compatible with the group operation. Lie group: a topological group with a...

category theory, topological algebra, homological algebra, Lie algebras, free algebras, and homology groups. The influence of algebra is wide reaching...

In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information...

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

homeomorphic to a real algebraic set. 1983 Akbulut and King introduced "Topological Resolution Towers" as topological models of real algebraic sets, from this...

to prove this theorem started the study of algebraic and topological K-theory, which explores the topological properties of objects by associating them...