Search results
Results from the WOW.Com Content Network
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 .
The real numbers form a topological group under addition. In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time, such that the continuity condition for the group operations connects these two structures together and consequently they are not independent from each other.
The product of two CW complexes can be made into a CW complex. Specifically, if X and Y are CW complexes, then one can form a CW complex X × Y in which each cell is a product of a cell in X and a cell in Y, endowed with the weak topology. The underlying set of X × Y is then the Cartesian product of X and Y, as expected.
Let G be a topological group, and for a topological space , write () for the set of isomorphism classes of principal G-bundles over .This is a contravariant functor from Top (the category of topological spaces and continuous functions) to Set (the category of sets and functions), sending a map : to the pullback operation : ().
The following table summarizes the separation axioms as well as the implications between them: cells which are merged represent equivalent properties, each axiom implies the ones in the cells to its left, and if we assume the T 1 axiom, then each axiom also implies the ones in the cells above it (for example, all normal T 1 spaces are also ...
A connected topological space X is called an Eilenberg–MacLane space of type (,), if it has n-th homotopy group isomorphic to G and all other homotopy groups trivial. Assuming that G is abelian in the case that n > 1 {\displaystyle n>1} , Eilenberg–MacLane spaces of type K ( G , n ) {\displaystyle K(G,n)} always exist, and are all weak ...
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 property of points in a topological space is said to be "open" if those points which possess it form an open set. Such conditions often take a common form, and that form can be said to be an open condition ; for example, in metric spaces , one defines an open ball as above, and says that "strict inequality is an open condition".