An irreducible component of a topological space 
is a maximal irreducible subset,
where a subset is irreducible if it is a nonempty
set and cannot be written as the union of two proper
closed subsets in its relative
topology (Stacks Project, Tag 004U). Every irreducible component is a closed
set, and 
is the union of its irreducible components. Each irreducible
component is connected, but distinct irreducible
components can intersect.
For example, the plane curve 
over an algebraically
closed field, with its Zariski
topology, has two irreducible components, the lines 
and 
, which meet at the origin. Thus
irreducible components need not be connected components.
