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 $X$. | ||
Revision as of 20:10, 17 January 2021
{[MSC|54G12}}
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=51384
Right separated space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Right_separated_space&oldid=51384