Answer to Question #323582 in Differential Geometry | Topology for Arshi

Question

Show that {𝑥} ⊆ ℝ is connected.

Answer 1

It should be proved that there is no such partition of {x} into two nonempty subsets which are open in the relative topology induced on {x}. Since if the first set contains x, the second subset is empty, there is no partition into nonempty subsets at all, hence {x} is connected.