We obtain characterizations of nearly strong convexity and nearly very convexity by using the dual concept of S and WS points, related to the so-called Rolewicz’s property (α). We give a characterization of those points in terms of continuity properties of the identity mapping. The connection between these two geometric properties is established, and finally an application to approximative compactness is given.

中文翻译：

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近强和近极凸空间的一些度量和拓扑性质

通过使用与所谓的Rolewicz属性（α）有关的S点和WS点的对偶概念，我们获得了近乎强凸性和近乎非常凸性的特征。我们根据身份映射的连续性对这些点进行表征。建立了这两个几何特性之间的联系，最后给出了近似紧凑性的应用。