algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...

, a branch of mathematics, an approximate fibration is a sort of fibration such that the

homotopy lifting property In mathematics, in particular in homotopy theory within algebraic topology, the homotopy lifting property (also known as an instance of the right lifting property or the covering homotopy axiom) is a technical condition on a continuous function from ...

holds only approximately. The notion was introduced by Coram and Duvall in 1977. A manifold approximate fibration is a proper approximate fibration between manifolds. Some authors believe that manifold approximate fibrations are the "correct bundle theory for topological manifolds and singular spaces".

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