Concerning Cut Points Spaces of Order Three
by
William S. Mahavier
Dept. of Mathematics and CS, Emory University, Atlanta, GA 30322
Coauthors: Dale Daniel

A point p of a topological space S is a cut point of order 3 if and only if S-{p} is the union of three mutually exclusive connected sets. We construct a connected Hausdorff S space such that each point of S is a cut point of order 3. We also show that if S is a separable connected Hausdorff space, then S does not contain uncountable many points of cut point order 3.

Date received: February 28, 2005