In this paper, we deal with analytic and geometric properties of orthogonally convex sets. We establish a Blaschke-type theorem for path-connected and orthogonally convex sets in the plane using orthogonally convex paths. The separation of these sets is established using suitable grids. Consequently, a closed and orthogonally convex set is represented by the intersection of staircase-halfplanes in the plane. Some topological properties of orthogonally convex sets in dimensional spaces are also given.

翻译：在本文中,我们处理的是正方形螺旋形的分析和几何特性。我们用正方形螺旋形的路径,为平面上与路径相连的和正方形螺旋形的螺旋形装置建立一个布拉施克型的理论原理。这些装置的分离是使用合适的网格确定的。因此,封闭的和正方形螺旋形装置由平面上平面上的双翼平面图的交叉表示。还给出了各维空间中正方形螺旋形装置的一些地形特性。