For any open, fiberwise dense first-order differential relation, every piecewise smooth section can be epsilon-jiggled to a solution, and the space of piecewise solutions is weakly equivalent to the space of continuous sections.
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Jiggling: an h-principle without homotopical assumptions
For any open, fiberwise dense first-order differential relation, every piecewise smooth section can be epsilon-jiggled to a solution, and the space of piecewise solutions is weakly equivalent to the space of continuous sections.