Cofibrations in the category of Frölicher spaces: Part I

Abstract

Cofibrations are defined in the category of Frölicher spaces by weakening the analog of the classical definition to enable smooth homotopy extensions to be more easily constructed, using flattened unit intervals. We later relate smooth cofibrations to smooth neighborhood deformation retracts. The notion of smooth neighborhood deformation retract gives rise to an analogous result that a closed Frölicher subspace A of the Frölicher space $X$ is a smooth neighborhood deformation retract of $X$ if and only if the inclusion $i:A\hookrightarrow X$ comes from a certain subclass of cofibrations. As an application we construct the right Puppe sequence.