Hausdorff space

It is hard to define emptiness. Hausdorff space is known as empty set Φ.



X is a topological space.

X=(x,y)

x and y are dots.

U∩V=Φ

U is vicinities of x.
V is vicinities of y.

X×X→Δ={(x,x)|x∈X} is closed.