Discussion About Some Properties In The Width Of The Locally Convex Spaces

We usually study the widths on the normed spaces, which having good properties and causing a limitation of the study. For a expanding of the width of the study, we generalize the concept of width to the locally convex spaces and obtain some new results. In the past of the introduction, we introduce the properties of locally convex spaces, and the concept of width.In the text , we discuss the f-n-k width on the normed spaces. And we obtain aconversion theorem. We also obtain of the width of the unit ball of the locally convex spaces. And generalize the Brown s theorem to the locally convex spaces. So we obtain the perfect results of the width on the locally convex spaces.