  Inducing a magnetic gap at the Dirac point of the topological surface state
(TSS) in a 3D topological insulator (TI) is a route to dissipationless charge
and spin currents. Ideally, magnetic order is present only at the surface and
not in the bulk, e.g. through proximity of a ferromagnetic (FM) layer. However,
such a proximity-induced Dirac mass gap has not been observed, likely due to
insufficient overlap of TSS and the FM subsystem. Here, we take a different
approach, namely FM extension, using a thin film of the 3D TI Bi$_2$Te$_3$,
interfaced with a monolayer of the lattice-matched van der Waals ferromagnet
MnBi$_2$Te$_4$. Robust 2D ferromagnetism with out-of-plane anisotropy and a
critical temperature of $\text{T}_\text{c}\approx$~15 K is demonstrated by
X-ray magnetic dichroism and electrical transport measurements. Using
angle-resolved photoelectron spectroscopy, we observe the opening of a sizable
magnetic gap in the 2D FM phase, while the surface remains gapless in the
paramagnetic phase above T$_c$. This sizable gap indicates a relocation of the
TSS to the FM ordered Mn moments near the surface, which leads to a large
mutual overlap.
