__Glueing Lemma:__
Let X = A ∪ B, where A and B are closed in X.
Let f: A → Y and g: B → Y
be continuous. If f(x) = g(x) for every
x ∈ A ∩ B, then f and g combine
to give a continuous function h: X → Y,
defined by setting h(x) = f(x) if x ∈ A,
and h(x) = g(x) if x ∈ B.