  In [1] we introduced the notion of 'structured space', i.e. a space which
locally resembles various algebraic structures. In [2] and [3] we studied some
cohomology theories related to these space. In this paper we continue in this
direction: while in [2] we mainly focused on cohomologies arising from $f_s$
and $h$, and in [3] we considered cohomologies for generalisations of objects
which involved structured spaces, here we deal with (co)homologies coming from
the poset associated to a structured space via an equivalence relation defined
at the end of Section 4 in [1]. More precisely, we will show that various
(co)homologies for posets can also be applied (under some assumptions) to
structured spaces.
