The topologist's sine curve has this property, but not the related "local" property or the stricter "path" property.
The real line under the K-topology is Hausdorff and has this property, but is neither regular nor normal. The generalized intermediate value theorem applies to spaces with this property, since it is preserved by the action of continuous functions. Spaces with this property are precisely those for which the only sets that are both open and closed are the empty set and the space itself. Spaces with the "simply-" type of this property have the trivial fundamental group. The topologist's sine curve has this property, but not the related "local" property or the stricter "path" property. Formally, a topological space has this property if it cannot be partitioned into two disjoint nonempty open subsets. A space that lacks this property can be split into components. For 10 points, give this word that also describes a graph in which every vertex can be reached from every other vertex.
The real line under the K-topology is Hausdorff and has this property, but is neither regular nor normal.
connectedness [accept word forms like connected] &lt;Other Science (Math)&gt;