A Note on Non-cut Points, VH-sets, Almost VH-sets and COTS - Devender Kumar Kamboj (International Journal of Mathematics And its Applications, 2025)
Two concepts of VH-sets and almost VH-sets are introduced to study connected ordered topological spaces (COTS). We show that every R(i) subset of a connected space is an almost VH-set. Two characterizations of COTS with endpoints using the concept of almost VH-set have been obtained. It is also proved that if X is a connected non-cut point inclined space and the removal of any two-point disconnected set of it leaves the space disconnected, then each one of H {a, b} and K {a, b} has exactly two non-cut points, and is homeomorphic to a finite connected subspace of the Khalimsky line where H and K are separating sets of X {a, b}, a, b X.