I am studying an Amazonian language, Palikur, whose speakers think of objects in terms of their outside and inside. The language describes these two attributes according to their openness or compactedness, i.e. being open, or partially open, or closed. Palikur grammar classifies all inanimate entities according to their interior, boundary, and extendedness.
The language uses suffixes on numbers, verbs, adjectives, and prepositions to indicate the topology of the noun they refer to. One of the most common Palikur suffixes is -iku (if focus is on holes or the hollow interior of an item), for example:
One-iku well (or corral or room or ring)
Clean-iku the well! "
The well is clean-iku. "
Water is in-iku the well. "
The numerical terms also have suffixes that cover nine arithmetic operators (such as multiplication) and many other mathematical symbols which topologists use, for example, the concept of a set of all points in a or b (a ᑌ b) is –mat. the concept of a set of all points in a and b (a ᑎ b) is –nam; the concept that a is not a subset of b (a\ᑕ b) is –put; the n° of elements in a set (n(a)) is -at. Other suffixes indicate four types of symmetry. Palikur also has a word for lattice, ka-yakni-bet-ape (HAVING-CENTRAL.VERTEX-AGG-ALL) ‘having a set of central vertices, all intersected.’ In all, this extremely unusual language has almost a hundred topologically related suffixes.
Unfortunately, I am a linguist, not a topologist, so I really need help!