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This article defines a property of continuous maps between topological spaces


A continuous map p:E \to B of topological spaces is termed a fibration or is said to have the homotopy lifting property if it is surjective and, given any map F:X \times I \to B and a map \tilde{f}: X \to E such that p(\tilde{f}(x)) = f(x,0), there exists a map \tilde{F}:X \times I \to E satisfying:

  • p \circ \tilde{F} = F
  • F(x,0) = \tilde{f}(x)

This is dual to the notion of a cofibration.

Relation with other properties

Weaker properties