Yes, TOPOLOGIES is a Scrabble word!

Letter values in Scrabble US: T 1, O 1, P 3, O 1, L 1, O 1, G 2, I 1, E 1, S 1.

Is it a valid word?

TOPOLOGIES is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

topographic study of a given place (especially the history of the place as indicated by its topography)
the study of anatomy based on regions or divisions of the body and emphasizing the relations between various structures (muscles and nerves and arteries etc.) in that region
the branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions
the configuration of a communication network

Also: regional anatomy, topographic anatomy, analysis situs, network topology.