The hybrid topology on ${\mathcal{X}}^{\mathrm{hyb}}:=({\mathcal{X}}\setminus D)\cup\Delta(D)$ is defined as the coarsest topology such that:

• (i)

  ${\mathcal{X}}\setminus D\hookrightarrow{\mathcal{X}}^{\mathrm{hyb}}$ is an open embedding;

• (ii)

  For every open neighborhood ${\mathcal{V}}$ of $D$ in ${\mathcal{X}}$, the set $({\mathcal{V}}\setminus D)\cup\Delta({\mathcal{X}})$ is open in ${\mathcal{X}}^{\mathrm{hyb}}$;

• (iii)

  $\operatorname{Log}_{\mathcal{V}}\colon{\mathcal{V}}^{\mathrm{hyb}}\to\Delta(D)$ is continuous.