Di-uniformities and Hutton uniformities

The authors characterize di-uniformities on a texture (S,S) in the sense of Özçağ and Brown (Di-uniform texture spaces, Appl. Gen. Top. 4(1) (2003), 157–192) in terms of functions on the texturing S. This characterization enables quasi-uniformities in the sense of Hutton (Uniformities on Fuzzy Topological Spaces, J. Math. Anal. Appl. 58 (1977) 559–571) to be regarded as di-uniformities on the corresponding Hutton Texture, thereby revealing di-uniformities as a generalization of Hutton quasi-uniformities. The effect of imposing a complementation on (S,S) is also considered and several important results established.