Commutative monads as a theory of distributions
... T -algebras deserve the name T -linear spaces, and homomorphisms deserve the name T linear maps (and, if T is understood from the context, the ‘T ’ may even be omitted). This allows us to talk about partial T -linear maps, as well as T -bilinear maps, as we shall explain. An example of a commutative ...
... T -algebras deserve the name T -linear spaces, and homomorphisms deserve the name T linear maps (and, if T is understood from the context, the ‘T ’ may even be omitted). This allows us to talk about partial T -linear maps, as well as T -bilinear maps, as we shall explain. An example of a commutative ...
Topology Proceedings 1 (1976) pp. 351
... erated by Y is closed. We now turn to considering the topological structure of G II H for Hausdorff groups G and H. ...
... erated by Y is closed. We now turn to considering the topological structure of G II H for Hausdorff groups G and H. ...
Automorphism Groups
... I claim that there is an element of order 5 and an element of order 2. First, suppose every element besides 0 has order 2. Consider distinct elements a and b, a, b 6= 0. Look at the subgroup ha, bi. I’ll show that ha, bi = {0, a, b, a + b}. Since 2a = 2b = 0, it is easy to see by checking cases that ...
... I claim that there is an element of order 5 and an element of order 2. First, suppose every element besides 0 has order 2. Consider distinct elements a and b, a, b 6= 0. Look at the subgroup ha, bi. I’ll show that ha, bi = {0, a, b, a + b}. Since 2a = 2b = 0, it is easy to see by checking cases that ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.