Mazur spaces, which are locally convex spaces and every sequentially continuous linear functional over them is continuous,are characterized. The following results are obtained, if (X, T) is a locally convex space, the...Mazur spaces, which are locally convex spaces and every sequentially continuous linear functional over them is continuous,are characterized. The following results are obtained, if (X, T) is a locally convex space, then the followings are equivalent: 1) (X, T) is a Mazur space; 2) T + (the largest locally convex topology with the same convergent sequence as T) is a compatible topology with T; 3) every sequentially open half-space in (X, T) is open. The relation between Mazur spaces and C-sequential spaces is discussed.展开更多
文摘Mazur spaces, which are locally convex spaces and every sequentially continuous linear functional over them is continuous,are characterized. The following results are obtained, if (X, T) is a locally convex space, then the followings are equivalent: 1) (X, T) is a Mazur space; 2) T + (the largest locally convex topology with the same convergent sequence as T) is a compatible topology with T; 3) every sequentially open half-space in (X, T) is open. The relation between Mazur spaces and C-sequential spaces is discussed.
