Abstract

The importance of the theory of bitopological spaces is fully demonstrated by its natural relationship to the theory of ordered topological spaces. Using the parallels drawn by M. Canfell and T. McCallion between the theory of bitopological spaces and that of ordered topological spaces, we construct the dimension theory for ordered topological spaces and formulate and study the Baire-like properties of the latter spaces, thereby filling in the gap of the theory of ordered topological spaces. Further, based on these parallels, the relations between the separation axioms of ordered topological spaces and the corresponding bitopological spaces are established.

Keywords: $(l,u)$- and $(u,l)$-boundaries, a hereditarily strong normally ordered space, $l$- and $u$-nowhere dense sets, $l$- and $u$-first (second) category set, $l$- and $u$-Baire spaces.

MSC: 54F05, 54E55

Pages:  37--52     

Volume  55 ,  Issue  1$-$2 ,  2003