Editing Suslin's problem (section)

==Formulation==
Suslin's problem asks: Given a [[non-empty]] [[totally ordered set]] ''R'' with the four properties
# ''R'' does not have a [[greatest element and least element|least nor a greatest element]];
# the order on ''R'' is [[dense order|dense]] (between any two distinct elements there is another);
# the order on ''R'' is [[completeness (order theory)|complete]], in the sense that every non-empty bounded subset has a [[supremum]] and an [[infimum]]; and
# every collection of mutually [[disjoint sets|disjoint]] non-empty [[open interval]]s in ''R'' is [[countable]] (this is the [[countable chain condition]] for the [[order topology]] of ''R''),
is ''R'' necessarily [[order isomorphism|order-isomorphic]] to the [[real line]] '''R'''?

If the requirement for the countable chain condition is replaced with the requirement that ''R'' contains a countable dense subset (i.e., ''R'' is a [[separable space]]), then the answer is indeed yes: any such set ''R'' is necessarily order-isomorphic to '''R''' (proved by [[Georg Cantor|Cantor]]).

The condition for a [[topological space]] that every collection of non-empty disjoint [[open set]]s is at most countable is called the '''Suslin property'''.