Title: Succinctness in subsystems of the spatial mu-calculus,
Abstract: In this paper we systematically explore questions of succinctness in modal
logics employed in spatial reasoning. We show that the closure operator,
despite being less expressive, is exponentially more succinct than the
limit-point operator, and that the $\mu$-calculus is exponentially more
succinct than the equally-expressive tangled limit operator. These results hold
for any class of spaces containing at least one crowded metric space or
containing all spaces based on ordinals below $\omega^\omega$, with the usual
limit operator. We also show that these results continue to hold even if we
enrich the less succinct language with the universal modality.