Author/Authors :
Kubiak، نويسنده , , Tomasz، نويسنده ,
Abstract :
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- T 0 separation axiom of Liu and the L - T 0 separation axiom of Rodabaugh.
Keywords :
Sub- T 0 axiom , L - T 0 axiom , Subbase , L-Tychonoff space , Embedding theorem , Subbasic characterization , Weight , L-real line , Unit L-interval , Insertion theorem , COMPACT , extension theorem , Meet-continuous lattice , Order reversing involution , Completely L-regular space , Topology
