Cut-point spaces
B. Honari, Yousef Bahrampour · Proceedings of the American Mathematical Society · 1999
The notion of a cut-point space is introduced as a connected topological space without any non-cut point. It is shown that a cut-point space is infinite. The non-cut point existence theorem is proved for general (not necessarily T 1 T_1 ) topological spaces to show that a cut-point space is non-compact. Also, the class of irreducible cut-point spaces is studied and it is shown that this class (up to homeomorphism) has exactly one member: the Khalimsky line.