Suslin's problem [SEP] named after
Suslin's problem
In mathematics, Suslin's problem is a question about totally ordered sets posed by and published posthumously.
It has been shown to be independent of the standard axiomatic system of set theory known as ZFC: showed that the statement can neither be proven nor disproven from those axioms, assuming ZF is consistent.
Formulation.
Given a non-empty totally ordered set "R" with the following four properties:
1. "R" does not have a least nor a greatest element;
condition.
Examples and properties in topology.
A topological space is said to satisfy the countable chain condition, or Suslin's Condition, if the partially ordered set of non-empty open subsets of "X" satisfies the countable chain condition, "i.e." every pairwise disjoint collection of non-empty open subsets of "X" is countable. The name originates from Suslin's Problem.
- Every separable topological space is ccc. Furthermore, the product space of at most formula_1 separable spaces is a separable space