Some separation axioms in L-topological spaces (Q2915802)

Based on the idea sub-\(T_0\) which was introduced by Y.M.Liu in 1983, the authors propose five new separation axioms: sub-\(T_1\), sub-\(T_2\), sub-\(T_{2\frac{1}{2}}\), sub-\(T_3\) and sub-\(T_4\) in \(L\)-topological spaces and show that these sub-separation axioms are good extensions in the sense of Lowen. In last section, the authors use more examples to show that sub-separation axioms and other separation axioms are quite different, and prove that sub-\(T_1\) implies Kubiak-\(T_1\) and layer-\(T_1\) implies sub-\(T_1\) in an \(L\)-topological space without any condition.