Right separated space

2020 Mathematics Subject Classification: Primary: 54G12 [MSN][ZBL]

A topological space $X$ is right (resp. left) separated if there is a well ordering ${<}$ on $X$ such that the segments $\{x \in X : x < y\}$ are all open (resp. closed) in the topology of $X$.

A Hausdorff space is scattered if and only if it is right separated.

References

• Sheldon W. David, "Topology", McGraw-Hill (2005) ISBN 0072910062