homotopy property

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• Homotopy lifting property — In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a… …   Wikipedia

• Homotopy — This article is about topology. For chemistry, see Homotopic groups. The two dashed paths shown above are homotopic relative to their endpoints. The animation represents one possible homotopy. In topology, two continuous functions from one… …   Wikipedia

• Homotopy extension property — In mathematics, in the area of algebraic topology, the homotopy extension property indicates when a homotopy can be extended to another one, so that the original homotopy is simply the restriction of the extended homotopy.DefinitionGiven A subset …   Wikipedia

• Homotopy group — In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The base point preserving maps from an n dimensional sphere (with base point) into a given space (with base point) are collected into equivalence… …   Wikipedia

• Homotopy principle — In mathematics, the homotopy principle (or h principle) is a very general way to solve partial differential equations (PDEs), and more generally partial differential relations (PDRs). The h principle is good for underdetermined PDEs or PDRs, such …   Wikipedia

• Rational homotopy theory — In mathematics, rational homotopy theory is the study of the rational homotopy type of a space, which means roughly that one ignores all torsion in the homotopy groups. It was started by Dennis Sullivan (1977) and Daniel Quillen (1969) …   Wikipedia

• A¹ homotopy theory — In algebraic geometry and algebraic topology, a branch of mathematics, A1 homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes. The theory is due to… …   Wikipedia

• Model category — In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ( arrows ) called weak equivalences , fibrations and cofibrations . These abstract from a conventional homotopy category, of… …   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

• Classifying space — In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e. a topological space for which all its homotopy groups are trivial) by a free action of G. It… …   Wikipedia

• List of mathematics articles (H) — NOTOC H H cobordism H derivative H index H infinity methods in control theory H relation H space H theorem H tree Haag s theorem Haagerup property Haaland equation Haar measure Haar wavelet Haboush s theorem Hackenbush Hadamard code Hadamard… …   Wikipedia