Spaces that are intersections of chains of locally bicompact spaces (Q1056943)

A family of sets \(\xi\) is called a chain if for every A,B\(\in \xi\) it is true that \(A\subset B\) or \(B\subset A\). Properties of spaces which can be expressed as the intersection of a chain of spaces of a class \({\mathcal P}\) are investigated (\({\mathcal P}\) is closed under perfect mappings). Some statements about spaces which can be expressed as an intersection of a chain of locally compact spaces are proved, e.g., if X has compactification with separable remainder and is an intersection of a chain of locally compact spaces then X is a Čech-complete space.