  The realization of Bose-Einstein condensation in ultracold trapped gases has
led to a revival of interest in that fascinating quantum phenomenon. This
experimental achievement necessitated both extremely low temperatures and
sufficiently weak interactions. Particularly in reduced spatial dimensionality
even an infinitesimal interaction immediately leads to a departure to
quasi-condensation. We propose a system of strongly interacting bosons which
overcomes those obstacles by exhibiting a number of intriguing related
features: (i) The tuning of just a single control parameter drives a transition
from quasi-condensation to complete condensation, (ii) the destructive
influence of strong interactions is compensated by the respective increased
mobility, (iii) topology plays a crucial role since a crossover from one- to
`infinite'-dimensionality is simulated, (iv) a ground state gap opens which
makes the condensation robust to thermal noise. Remarkably, all these features
can be derived by analytical and exact numerical means despite the
non-perturbative character of the system.
