This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological spaceView a complete list of properties of topological spaces
Definition
A topological space is termed linearly orderable if it occurs as the underlying topological space of a linearly ordered space (viz it can be obtained by giving the order topology to a linearly ordered set).
Relation with other properties
Weaker properties
Property 
Meaning 
Proof of implication 
Proof of strictness (reverse implication failure) 
Intermediate notions

monotonically normal space 



FULL LIST, MORE INFO

hereditarily normal space 
every subspace is a normal space 
(via monotonically normal) 
(via monotonically normal) 
Hereditarily collectionwise normal space, Monotonically normal spaceFULL LIST, MORE INFO

normal space 
and disjoint closed subsets can be separated by disjoint open subsets 
(via monotonically normal) 
(via monotonically normal) 
Collectionwise normal space, Hereditarily collectionwise normal space, Hereditarily normal space, Monotonically normal spaceFULL LIST, MORE INFO

completely regular space 



Monotonically normal space, Normal Hausdorff spaceFULL LIST, MORE INFO

regular space 



Monotonically normal space, Normal Hausdorff spaceFULL LIST, MORE INFO

Hausdorff space 
distinct points can be separated by disjoint open subsets 
linearly orderable implies Hausdorff, also via others 
(via regular, normal) 
Monotonically normal space, Normal Hausdorff spaceFULL LIST, MORE INFO

T1 space 
points are closed 
linearly orderable implies T1, also via Hausdorff 
(via Hausdorff, others) 
Normal Hausdorff spaceFULL LIST, MORE INFO
