  We consider simplicial sets equipped with a notion of smallness, and observe
that this slight "topological" extension of the "algebraic" simplicial language
allows a concise reformulation of a number of classical notions in topology,
e.g. continuity, limit of a map or a sequence along a filter, various notions
of equicontinuity and uniform convergence of a sequence of functions;
completeness and compactness; in algebraic topology, locally trivial bundles as
a direct product after base-change and geometric realisation as a space of
discontinuous paths.
  In model theory, we observe that indiscernible sequences in a model form a
simplicial set with a notion of smallness which can be seen as an analogue of
the Stone space of types.
  These reformulations are presented as a series of exercises, to emphasise
their elementary nature and that they indeed can be used as exercises to make a
student familiar with computations in basic simplicial and topological
language. (Formally, we consider the category of simplicial objects in the
category of filters in the sense of Bourbaki.)
  This work is unfinished and is likely to remain such for a while, hence we
release it as is, in the small hope that our reformulations may provide
interesting examples of computations in basic simplicial and topological
language on material familiar to a student in a first course of topology or
category theory.
