  We prove a certain 'fat hyperplane section' Weak Lefschetz-type theorem for
etale cohomology of non-projective varieties, similar to a result of Goresky
and MacPherson (over complex numbers). This statement easily yields certain
(vast) generalizations of the 'ordinary' Weak Lefschetz and Barth's theorems in
arbitrary characteristic (that do not require any stratified Morse theory for
their proof).
