  Existing proximity effects stem from systems with a local order parameter,
such as a local magnetic moment or a local superconducting pairing amplitude.
Here, we demonstrate that despite lacking a local order parameter, topological
phases also may give rise to a proximity effect of a distinctively inverted
nature. We focus on a general construction in which a topological phase is
extensively coupled to a second system, and we argue that in many cases, the
inverse topological order will be induced on the second system. To support our
arguments, we rigorously establish this "bulk topological proximity effect" for
all gapped free fermion topological phases and representative integrable models
of interacting topological phases. We present a terrace construction which
illustrates the phenomenological consequences of this proximity effect.
Finally, we discuss generalizations beyond our framework, including how
intrinsic topological order may also exhibit this effect.
