Topological transitivity is a weaker version of topological mixing. K-theory studies the isomorphism classes of all vector bundles over some topological space. There, groups are used to describe certain invariants of topological spaces. These algebraic ideas are closely related to topological ideas. This construction makes all sheaves into representable functors on certain categories of topological spaces. Homeomorphisms are the isomorphisms in the category of topological spaces. This means that spacetime is a set of points enriched by topological and geometric structures. This is usually achieved by topologically sorting expressions and updating values in topological order. The set of open subsets of a topological space determines a lattice. The theorem also has consequences for broader classes of topological groups. Therefore, every graph with a topological ordering is acyclic. It is common to place additional requirements on topological manifolds. Triangulation is useful in determining the properties of a topological space. Isomorphisms of the topological plane are all continuous bijections. Kahn's algorithm for topological sorting builds the vertex ordering directly.