On $k$-connected Sets in Matroids

In 1966, Tutte defined $k$-connected matroids for each $k \ge 2$. Robertson and Seymour built on Tutte's idea to define tangles as a way to identify highly connected parts of a matroid. Motivated by tangles, a set $Z$ in a matroid $M$ has been defined to be $3$-connected if, for each $j$ in $\{1,2\}