Math and science::Topology

# Connectedness. Definition

### Connectedness

Let $$X$$ be a topological space. A [...] of $$X$$ is a pair $$U, V$$ of disjoint nonempty open subsets of $$X$$ whose union is $$X$$. The space $$X$$ is said to be connected iff [...].

This definition is from Munkres. Leinster's definition feels a little less intuitively concrete.

#### Connectedness, formulation 2 (or now a lemma)

A space $$X$$ is connected iff the only subsets of $$X$$ that [...] are [...].

Again, from Munkres.