A space has the opposite of this property if it can be expressed as the union of two disjoint open sets.
Kyrmse proposed the term  polynema  to describe graphs which have this property and some  xed number of edges. The topologist's sine curve has this property, but is not locally this. A space is said to be hyper-this if no two open sets are   disjoint. A space has the opposite of this property if it can be expressed as the union of two disjoint open sets. The real line has this property, but if any point is removed, it loses this property. For ten points, identify this property, whose path version is possessed by a space if there exists a path between any two points in the space lying entirely within the space.
Kyrmse proposed the term  polynema  to describe graphs which have this property and some  xed number of edges.
connectedness [accept word forms]