covering homotopy - определение. Что такое covering homotopy
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Что (кто) такое covering homotopy - определение

IN ALGEBRAIC TOPOLOGY
Covering homotopy; Covering homotopy axiom
  • center

Homotopy lifting property         
In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as an instance of the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a topological space E to another one, B. It is designed to support the picture of E "above" B by allowing a homotopy taking place in B to be moved "upstairs" to E.
Covering group         
CONCEPT IN TOPOLOGICAL GROUP THEORY
Universal covering group; Covering homomorphism; Double covering group; Lattice of covering groups; Abelian covering
In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map is a continuous group homomorphism. The map p is called the covering homomorphism.
Covering space         
  • frameless
  • Intuitively, a covering locally projects a "stack of pancakes" above an [[open neighborhood]] <math>U</math> onto <math>U</math>
TYPE OF CONTINUOUS MAP IN TOPOLOGY
Universal cover; Universal covers; Universal Cover; Universal covering; Deck transformation group; Universal covering space; Deck transformation; Galois covering; Covering map; Covering transformation; Covering maps; Double cover (topology); Deck transformations; Universal coverings; Galois theory of covering spaces; Simply connected covering; Regular covering; Regular cover; Regular covering group
A covering of a topological space X is a continuous map \pi : E \rightarrow X with special properties.

Википедия

Homotopy lifting property

In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as an instance of the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from a topological space E to another one, B. It is designed to support the picture of E "above" B by allowing a homotopy taking place in B to be moved "upstairs" to E.

For example, a covering map has a property of unique local lifting of paths to a given sheet; the uniqueness is because the fibers of a covering map are discrete spaces. The homotopy lifting property will hold in many situations, such as the projection in a vector bundle, fiber bundle or fibration, where there need be no unique way of lifting.