Difference between revisions of "Right separated space"
From Encyclopedia of Mathematics
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A [[topological space]] $X$ is '''right''' (resp. '''left''') '''separated''' if there is a [[Well-ordered set|well ordering]] ${<}$ on $X$ such that the segments $\{x \in X : x < y\}$ are all open (resp. closed) in the topology of $X$. | A [[topological space]] $X$ is '''right''' (resp. '''left''') '''separated''' if there is a [[Well-ordered set|well ordering]] ${<}$ on $X$ such that the segments $\{x \in X : x < y\}$ are all open (resp. closed) in the topology of $X$. | ||
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| − | * Sheldon W. David, "Topology", McGraw-Hill (2005) ISBN 0072910062 | + | * Sheldon W. David, "Topology", McGraw-Hill (2005) {{ISBN|0072910062}} |
Latest revision as of 12:00, 23 November 2023
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=51385
Right separated space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Right_separated_space&oldid=51385