Uniform Topological Spaces Based on BF-ideals in Negative Non-involutive Residuated Lattices

Abstract

In this paper, the uniform topological spaces are established based on the congruences induced by BF-ideals and some of their properties are discussed in negative non-involutive residuated lattices. The following conclusions are proved: (i) every uniform topological space is first-countable, zero-dimensional, disconnected, locally compact and completely regular. (ii) a uniform topological space is a T1 space iff it is a T2 space. (iii) the lattice and adjoint operations in a negative non-involutive residuated lattice are continuous with respect to the uniform topology, which make the negative non-involutive residuated lattice to be topological negative non-involutive residuated lattice. Meanwhile, some necessary and sufficient conditions for the uniform topological spaces to be compact and discrete are obtained. The results of this paper have a positive role to reveal internal features of negative non-involutive residuated lattices at a topological level.