On L-Tychonoff spaces II

This paper is a sequel to the 1995 paper On L-Tychonoff spaces. The embedding theorem for L-topological spaces is shown to hold true for L an arbitrary complete lattice without imposing any order reversing involution (·)′ on L. Some results on completely L-regular spaces and on L-Tychonoff spaces, which have previously been known to hold true for (L,′) a frame, are exhibited as ones holding for (L,′) a meet-continuous lattice. For such a lattice an insertion theorem for completely L-regular spaces is given. Some weak forms of separating families of maps are discussed. We also clarify the dependence between the sub-T0 separation axiom of Liu and the L-T0 separation axiom of Rodabaugh.