It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0...It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0, or 'lower semi-continuous' in some neighborhood V(x0) U0 and X is of second category; then p(x) can attain its supremum in U0. And there is a similar conclusion for the γ-max-subadditive functional when its supremum is 0 and if U0 is 'pseudo-bounded' set in X.展开更多
文摘It is shown that if a 'max-subadditive funtional' p(x) defined on some symmetric neighborhood U0 of zero vector θ in a 'b.f.-toplological group' X is 'upper semi-cotinuous' at a point x0 ∈ U0, or 'lower semi-continuous' in some neighborhood V(x0) U0 and X is of second category; then p(x) can attain its supremum in U0. And there is a similar conclusion for the γ-max-subadditive functional when its supremum is 0 and if U0 is 'pseudo-bounded' set in X.
