1. The Baire category theorem - Aarhus Universitet

Definition of first and second category
Let S be a topological space, i.e.
S is a set with a specified collection τ of subsets, the open sets,
such that
i) S, ∅ ∈ τ,
ii) when U1,U2,... ,Un is a finite number of elements of τ the
intersection
n
is also in τ.
i=1
iii) for any collection Uα,α ∈ I, of sets from τ the union
is also in τ.
α∈I
Ui
Uα
Klaus Thomsen 1. The Baire category theorem