Journal of the
Korean Mathematical Society JKMS

The aim of this paper is to study $L$-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between $L$-fuzzy co-topology and $L$-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when $\mathcal{U}$ is an $L$-fuzzy quasi-uniformity and they will be coincident when $\mathcal{U}$ is an $L$-fuzzy uniformity. It is also showed that each $L$-fuzzy co-topological space is $L$-fuzzy quasi-uniformizable.

Keywords: $L$-fuzzy co-topology, fuzzy remote neighborhood system, $L$-fuzzy (quasi-)uniformity

MSC numbers: 54E15, 54A40