In
mathematics, more specifically
algebraic topology, a
covering map (also
covering projection) is a
continuous function p from a
topological space,
C, to a topological space,
X, such that each point in
X has an
open neighbourhood
evenly covered by
p (as shown in the image); the precise definition is given below. In this case,
C is called a
covering space and
X the
base space of the covering projection. The definition implies that every covering map is a
local homeomorphism.