In mathematics, more specifically algebraic topology, the fundamental group ( defined by Henri Poincaré in his article Analysis Situs, published in 1895 ) is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

In mathematics, more specifically algebraic topology, a covering map is a continuous surjective function p from a topological space, C, to a topological space, X, such that each point in X has a neighbourhood evenly covered by p. This means that for each point x in X, there is associated an ordered pair, ( K, U ), where U is a neighborhood of x and where K is a collection of disjoint open sets in C, each of which gets mapped homeomorphically, via p, to U ( as shown in the image ).

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