π-Base shows that linear order topology is not normal. But I remember in class the prof said order topology is normal.
If $X$ is a set with linear order $<$, define a topology on X by letting $\{(a,b):a<b\}$ be a basis (where $(a,b)=\{x∈X:a<x<b\}$).
Asked
Active
Viewed 635 times
1
-
2See http://math.stackexchange.com/questions/322683/why-are-ordered-spaces-normal-collecting-proofs. It is even hereditarily normal. – Stefan Hamcke Apr 17 '15 at 16:26
-
2That entry is flat wrong. A LOTS (linearly ordered topological space with the order topology) is even hereditarily collectionwise normal, which is about as strong a normality property as you can get. – Brian M. Scott Apr 17 '15 at 18:52
1 Answers
0
As the comments note, every LOTS is normal. It's possible the pi-Base had such an error in 2015, but today it knows better.
Steven Clontz
- 8,773