topological chain
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Chain complex — Bicomplex redirects here. For the number, see Bicomplex number In mathematics, chain complex and cochain complex are constructs originally used in the field of algebraic topology. They are algebraic means of representing the relationships between … Wikipedia
Noetherian topological space — In mathematics, a Noetherian topological space is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the… … Wikipedia
Countable chain condition — See also: Forcing (set theory)#The countable chain condition In order theory, a partially ordered set X is said to satisfy the countable chain condition, or to be ccc, if every strong antichain in X is countable. There are really two conditions:… … Wikipedia
Homotopy category of chain complexes — In homological algebra in mathematics, the homotopy category K(A) of chain complexes in an additive category A is a framework for working with chain homotopies and homotopy equivalences. It lies intermediate between the category of chain… … Wikipedia
Covering space — A covering map satisfies the local triviality condition. Intuitively, such maps locally project a stack of pancakes above an open region, U, onto U. In mathematics, more specifically algebraic topology, a covering map is a continuous surjective… … Wikipedia
Singular homology — In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of topological invariants of a topological space X , the so called homology groups H n(X). Singular homology is a particular example of a… … Wikipedia
Homological algebra — is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract… … Wikipedia
Homology (mathematics) — In mathematics (especially algebraic topology and abstract algebra), homology (in Greek ὁμός homos identical ) is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a… … Wikipedia
Delta set — In mathematics, a delta set (or Δ set) S is a combinatorial object that is useful in the construction and triangulation of topological spaces, and also in the computation of related algebraic invariants of such spaces. A delta set is somewhat… … Wikipedia
Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… … Wikipedia
Soil food web — The soil food web is the community of organisms living all or part of their lives in the soil. It describes a complex living system in the soil and how it interacts with the environment, plants, and animals. Introduction Food webs describe the… … Wikipedia
