Topological frame extension

Abstract

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.