We define a $\sigma$-ideal $\mathscr{J_D}$ on the set of functions $^\omega\omega$ with the property that a real $x \in ^\omega\omega$ is a Hechler real over $\mathbf{V}$ if and only if $x$ omits all Borel sets in $\mathscr{J_D}$. In fact we define a topology $\mathscr{D}$ on $^\omega\omega$ related to Hechler forcing such that $\mathscr{J_D}$ is the family of first category sets in $\mathscr{D}$. We study cardinal invariants of the ideal $\mathscr{J_D}$.