Bitopological QHC spaces (Q923412)

The authors present several investigations on bitopological ij-QHC and pairwise QHC spaces, establish some characterizations of such spaces, define ij-regular spaces and use this property to study pairwise QHC spaces. Then they consider pairwise QHC spaces along with pairwise Urysohn spaces. They prove that (1) if \((X,Q_ 1,Q_ 2)\) is p-QHC and p-Urysohn, then X is p-almost regular and (2) if \((X,Q_ 1,Q_ 2)\) is p-QHC and p-Urysohn, then \((X,Q^ s_ 1)\) and \((X,Q^ s_ 2)\) are compact. They establish some other interesting theorems regarding these concepts and finally they introduce the concept of pairwise H-sets. Some characterizations and some other properties of ij-H-sets are proved too.