Right separated space
From Encyclopedia of Mathematics
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
How to Cite This Entry:
Right separated space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Right_separated_space&oldid=51386
Right separated space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Right_separated_space&oldid=51386