Difference between revisions of "Right separated space"
From Encyclopedia of Mathematics
(Start article: Right separated space) |
m (→References: isbn link) |
||
| (2 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
| − | {{TEX|done}}{ | + | {{TEX|done}}{{MSC|54G12}} |
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 $X$. | ||
| Line 6: | Line 6: | ||
==References== | ==References== | ||
| − | * 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=51384
Right separated space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Right_separated_space&oldid=51384