Abstract
Let
X be a
T
0
-space, we say that
X is
H-spectral if its
T
0
-compactification is spectral. This paper deal with topological properties of
H-spectral spaces. In the case of
T
1
-spaces the
T
0
-compactification coincides with the Wallman compactification. We give necessary and sufficient condition on the
T
1
-space
X in order to get its Wallman compactification spectral.