Much of the topological nature of these spaces is developed in the branches of topology known as Algebraic Topology and Differential Topology. Other important applications of topology include a number of fixed-point theorems and the topological nature of dynamical systems. Clearly many of the most-applicable research in this area is limited to metric spaces or manifolds, but some of the topics may be approached in a fairly general way. History See the article on Topology at St Andrews. Algebraic Topology for the definitions, and computations, and applications of fundamental groups, homotopy groups, homology and cohomology.
Simplicial complexes are essentially polyhedra .
Problems specific to Euclidean space may be treated in the geometry pages, particularly if the questions themselves center heavily on the metric. In particular, this includes the more detailed studies of dynamical systems, although the related area of fractals is most likely in Measure Theory . The study of topological vector spaces is treated in detail in functional analysis and related fields such as operator theory. There is also a separate classification for topological groups . Spaces with richer structures especially metric spaces.