Not normal topological spaces #
In this file we prove (see
IsClosed.not_normal_of_continuum_le_mk) that a separable space with a
discrete subspace of cardinality continuum is not a normal topological space.
s be a closed set in a separable normal space. If the induced topology on
s is discrete,
s has cardinality less than continuum.
The proof follows https://en.wikipedia.org/wiki/Moore_plane#Proof_that_the_Moore_plane_is_not_normal
s be a closed set in a separable space. If the induced topology on
s is discrete and
has cardinality at least continuum, then the ambient space is not a normal space.