A linear continuum L in the order topology has this property, and so do intervals and rays in L.
A linear continuum L in the order topology has this property, and so do intervals and rays in L. For a topological space X, the equivalence relation which holds for two points if they are both in some subspace with this property splits X into equivalence classes known as components. This property holds for a topological space if and only if it has no proper closed and open subsets. The general form of the Intermediate Value Theorem applies in the case of a continuous map to an ordered set in the order topology from a topological space with this property. For ten points, name this topological property which holds for spaces that cannot be expressed as the union of a pair of disjoint, nonempty, open sets, also known as a separation.
A linear continuum L in the order topology has this property, and so do intervals and rays in L.
Connectedness