The concept of nearness on a set was introduced by H. Herrlich. D. Le-
seberg generalized nearness by introducing supernearness, which generalizes also
supertopology as de ned by D. Doitchinov. In this paper, our work is based on the
representation theorem of M. H. Stone and the de nition of nearness. We de ne
proximity and nearness on a Boolean frame and then, by using these, we de ne
supertopic frame, supernear frame and paranear frame. We study basic properties
of the concepts de ned. We also introduce a topological extension on a Boolean
frame and investigate its behavior
