# Bundle map

From Topospaces

*This article defines a property of continuous maps between topological spaces*

## Contents

## Definition

A surjective continuous map is termed a **bundle map** or **fiber bundle** with fiber (where is an abstract topological space) if the following is true:

- The fiber at any point is homeomorphic to
- Every point in has an open neighbourhood such that the map
*looks like*the projection (this is called a*local triviality*condition)

If there is a homeomorphism from to under which gets sent to the projection map, then we say that the bundle map is trivial.

## Relation with other properties

### Stronger properties

- Covering map: This is a bundle map with discrete fibers