Riazanil näo lift

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.

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Lift. Given a map f from a space X to a space Y and another map g from a space Z to a space Y , a lift is a map h from X to Z such that gh=f In other words, a lift of f is a map h such that the diagram (shown below) commutes. Lift. If f is the identity from Y to Y , a manifold, and if g is the bundle projection from the tangent bundle .

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A basic example in topology is lifting a path in one space to a path in a covering space. Consider, for instance, mapping opposite points on a sphere to the same point, a continuous map from the sphere covering the projective plane. A path in the projective plane is a continuous map from the unit interval, [0,1]. We can lift .




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