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Let $k$ and $n$ be fixed, $k \geq 1$ , $n \geq 1$ , and let $S$ be a simply connected orthogonal polygon in the plane. For $T \subseteq S, T$ lies in a staircase $n$ -convex orthogonal polygon $P$ in $S$ if and only if every two points of $T$ see each other via staircase $n$ -paths in $S$ . This leads to a characterization for those sets $S$ expressible as a union of $k$ staircase $n$ -convex polygons $P_{i}$ , $1 \leq i \leq k$ .

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LNC points for m-convex sets.

A Helly number for unions of two boxes in $ℝ^{2}$ .

Characterizing certain staircase convex sets in $ℝ^{d}$ .

A staircase illumination theorem for orthogonal polygons.

Helly-type theorems for infinite and for finite intersections of sets starshaped via staircase paths.

Staircase Kernels for Orthogonal d-Polytopes.

Visible shorelines in Rd.

j-partitions for visible shorelines.

Sets Expressible as Unions of Staircase $n$ -Convex Polygons