Improved nearness research IV

Abstract

In some previous papers we studied generalized nearness by supernear spaces in connection with unifications and topological extensions, respectively. Now, this last part of series deals with those supernear spaces, which cover closely LODATO spaces, b-supertopologies and hence EF-proximities as well. Moreover, we will show that some special kind of these spaces have a local topological extension iff they are superbunch spaces. Consequently, this fundamental result leading us to a further generalization of LODATO's theorem, and in addition Doîtchinov's achievement can be dealt with, but in a modified fashion.