Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904055 | Topology and its Applications | 2018 | 14 Pages |
Abstract
The concept of cut point convex sets is used to study non-cut points of a connected topological space. Some relations between cut point convex sets, H-sets and COTS are established. We prove that an H-set of a COTS is contained in a COTS with endpoints a and b for some a, b in the H-set. It is shown that if a connected topological space X has at most two non-cut points and an R(i) set that contains all the closed cut points of X, then X is a COTS with endpoints. Further we show that if every non-degenerate proper regular closed connected subset of a connected topological space X contains only finitely many closed points of X, then X has at least two non-cut points. A characterization of a non-indiscrete finite connected subspace of the Khalimsky line is also obtained.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Devender Kumar Kamboj, Vinod Kumar,