Linear pointwise L-quasi uniformities

The main purpose of this paper is to study pointwise L-quasi uniformities on vector spaces. Firstly, we introduced a concept of linear pointwise L-quasi uniformities and proved that there is a one-to-one correspondence between the family of linear pointwise L-quasi uniformities and the set of L-topological vector spaces. More precisely, each linear pointwise L-quasi uniformity can generate a vector L-topology and every L-topological vector space is linear pointwise L-quasi uniformizable. Secondly, the Hausdorff separation and pointwise quasi-uniformly continuous of linear operators are investigated. In addition, as an example, the linear pointwise L-quasi uniformity induced by an L-fuzzy norm is also discussed.