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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.