Fortissimo space is defined by taking an uncountable set
X, with a particular point
p in
X, and declaring open the subsets
A of
X such that: •
A does not contain
p, or •
A contains all but a countable number of points of
X. The subspace X\setminus\{p\} has the discrete topology and is open and dense in
X. The space
X is not compact, but it is a
Lindelöf space. It is obtained by taking an uncountable discrete space, adding one point and defining a topology such that the resulting space is Lindelöf and contains the original space as a dense subspace. Similarly to Fort space being the one-point compactification of an infinite discrete space, one can describe Fortissimo space as the
one-point Lindelöfication of an uncountable discrete space. == See also ==