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We extend the well-known result that any $f \inW^{1,n}(\Omega,\mathbb{R}^n)$, $\Omega \subset \mathbb{R}^n$ with strictlypositive Jacobian is actually continuous: it is also true for fractionalSobolev spaces $W^{s,\frac{n}{s}}(\Omega)$ for any $s \geq \frac{n}{n+1}$,where the sign condition on the Jacobian is understood in a distributionalsense.  Along the way we also obtain extensions to fractional Sobolev spaces$W^{s,\frac{n}{s}}$ of the degree estimates known for $W^{1,n}$-maps withpositive or non-negative Jacobian, such as the sense-preserving property.

$W^{s,\frac{n}{s}}$-maps with positive distributional Jacobians