order compatible topology
1Order theory — For a topical guide to this subject, see Outline of order theory. Order theory is a branch of mathematics which investigates our intuitive notion of order using binary relations. It provides a formal framework for describing statements such as… …
2Cyclic order — In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order cannot be modeled as a binary relation a < b . One does not say that east is more clockwise than west.… …
3Grothendieck topology — In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a …
4Weak topology — This article discusses the weak topology on a normed vector space. For the weak topology induced by a family of maps see initial topology. For the weak topology generated by a cover of a space see coherent topology. In mathematics, weak topology… …
5Strahler Stream Order — The streams range from one (1) to the most powerful which is the Amazon River at 12. The Ohio River is an 8 and the Mississippi River is a 10. 80 percent of the streams and rivers on the planet are first or second order.To qualify as a stream it… …
6Limit-preserving function (order theory) — In the mathematical area of order theory, one often speaks about functions that preserve certain limits, i.e. certain suprema or infima. Roughly speaking, these functions map the supremum/infimum of a set to the supremum/infimum of the image of… …
7Algebraic structure — In algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The… …
8Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …
9Differentiable 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… …
10Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …
