This paper aims at providing further studies of the notion of quasi-relative interior for convex sets introduced by Borwein and Lewis. We obtain new formulas for representing quasi-relative interiors of convex graphs of set-valued mappings and for convex epigraphs of extended-real-valued functions defined on locally convex topological vector spaces. We also show that the role, which this notion plays in infinite dimensions and the results obtained in this vein, are similar to those involving relative interior in finite-dimensional spaces.

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In this paper, we show that the constant property of the Gaussian curvature of surfaces of revolution in both R 4 and R 4 1 depend only on the radius of rotation. We then give necessary and sufficient conditions for the Gaussian curvature of the general rotational surfaces whose meridians lie in two dimensional planes in R 4 to be constant, and define the parametrization of the meridians when both the Gaussian curvature is constant and the rates of rotation are equal.Mathematics Subject Classification. 53A05, 53C50, 53A35.

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