Search results
Results from the WOW.Com Content Network
An action of a topological group G on a topological space X is a group action of G on X such that the corresponding function G × X → X is continuous. Likewise, a representation of a topological group G on a real or complex topological vector space V is a continuous action of G on V such that for each g ∈ G, the map v ↦ gv from V to ...
Also, () is the group corresponding to vector bundles on the suspension of X. Topological K-theory is a generalized cohomology theory, so it gives a spectrum. The zeroth space is Z × B U {\displaystyle \mathbb {Z} \times BU} while the first space is U {\displaystyle U} .
In mathematics, a topological group G is a group that is also a topological space such that the group multiplication G × G→G and the inverse operation G→G are continuous maps. Subcategories This category has the following 2 subcategories, out of 2 total.
A set with a topology is called a topological space. Metric spaces are an important class of topological spaces where a real, non-negative distance, also called a metric, can be defined on pairs of points in the set. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.
In mathematics, topological modular forms (tmf) is the name of a spectrum that describes a generalized cohomology theory.In concrete terms, for any integer n there is a topological space , and these spaces are equipped with certain maps between them, so that for any topological space X, one obtains an abelian group structure on the set of homotopy classes of continuous maps from X to .
By definition, a generalized homology theory is a sequence of functors h i (for integers i) from the category of CW-pairs (X, A) (so X is a CW complex and A is a subcomplex) to the category of abelian groups, together with a natural transformation ∂ i: h i (X, A) → h i−1 (A) called the boundary homomorphism (here h i−1 (A) is a ...
A homology G-manifold (without boundary) of dimension n over an abelian group G of coefficients is a locally compact topological space X with finite G-cohomological dimension such that for any x∈X, the homology groups (,,) are trivial unless p=n, in which case they are isomorphic to G.
A locale is a sort of a space but perhaps not with enough points. [3] The topos theory is sometimes said to be the theory of generalized locales. [4]Jean Giraud's gros topos, Peter Johnstone's topological topos, [5] or more recent incarnations such as condensed sets or pyknotic sets.