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

redirect targets Topological group – Group that is a topological space with continuous group action Topological module Topological ring – ring where...

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

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

be generalized to topological modules. A subset A {\displaystyle A} of a topological module M {\displaystyle M} over a topological ring R {\displaystyle...

and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms...

In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures...

redirect targets Topological group – Group that is a topological space with continuous group action Topological module Topological ring – ring where...

any of several related functors on rings and modules that result in complete topological rings and modules. Completion is similar to localization, and...

homology theories for topological spaces that produce the same answer, one also often speaks of the homology of a topological space. (This latter notion...

mathematics, a metrizable space is a topological space that is homeomorphic to a metric space. That is, a topological space ( X , τ ) {\displaystyle (X,\tau...

This is a list of general topology topics. Topological space Topological property Open set, closed set Clopen set Closure Boundary Density G-delta set...

aforementioned block form. A topological vector space (TVS) X , {\displaystyle X,} such as a Banach space, is said to be a topological direct sum of two vector...

{\displaystyle X} into a topological vector space). Every topological vector space (TVS) X {\displaystyle X} is an additive commutative topological group but not...

persistence module is a mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological features...

redirect targets Topological group – Group that is a topological space with continuous group action Topological module Topological ring – ring where...

Connectedness is one of the principal topological properties that distinguish topological spaces. A subset of a topological space X {\displaystyle X} is a connected...

G} -module (it is an abelian group under addition). If G {\displaystyle G} is a topological group and M {\displaystyle M} is an abelian topological group...

of mathematics, locally convex topological vector spaces (LCTVS) or locally convex spaces are examples of topological vector spaces (TVS) that generalize...

to the topology, the module operations of addition and scalar multiplication are continuous, so that M becomes a topological module. However, M need not...

there are usually many different ways to construct a topological tensor product of two topological vector spaces. For Hilbert spaces or nuclear spaces...

the prime ideals of a commutative ring a topological space equipped with the Zariski topology; this topological space is called the spectrum of the ring...

redirect targets Topological group – Group that is a topological space with continuous group action Topological module Topological ring – ring where...

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

It is in this form that the regular representation is generalized to topological groups such as Lie groups. The specific definition in terms of W is as...

functional analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological vector space (TVS) X that has a partial...

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

Poincaré), also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous...