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 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 to do with the fact that 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.

Read more about Homotopy Lifting Property:  Formal Definition, Generalization: The Homotopy Lifting Extension Property

Famous quotes containing the words lifting and/or property:

    Thales claimed that everything was water. He also put wine into water to sterilize it. Did he really believe he was putting water into water to sterilize it? Parmenides, like most Greeks, knew that wine was not water. But while lifting a glass of wine to his lips, he denied that motion was possible. Did he really believe that the glass was not moving when he lifted it?
    Avrum Stroll (b. 1921)

    The second property of your excellent sherris is the warming
    of the blood.
    William Shakespeare (1564–1616)