讲座内容：

Let $\mathcal{F}$ be a family of subsets of $\mathbb{R}^d$ (with $d \geq 2$ throughout). A set $M \subseteq \mathbb{R}^d$ is said to be $\mathcal{F}$-convex if, for any pair of distinct points $x, y \in M$, there exists a set $F \in \mathcal{F}$ such that $x, y \in F$ and $F \subseteq M$. We obtain $\Gamma$-convexity when $\mathcal{F}$ consists of $\Gamma$-paths, where a $\Gamma$-path is defined as the union of the two legs of an isosceles right triangle.

In this talk, we first characterize certain $\Gamma$-convex sets. Next, we investigate $\Gamma$-starshaped sets and $\Gamma$-convexity partitions. Finally, we turn our attention to $\Gamma$-triple-convexity.