Original sentence: Both the infinite broom and its closure are connected, yet neither are locally connected.Despite the closed infinite broom being arc connected, the infinite broom is not path connected
Edited sentence: Both the infinite broom and its closure are connected, as every open set in the plane which contains the segment on the x-axis must intersect slanted segments.Despite the closed infinite broom being arc connected, the standard infinite broom is not path connected.Neither are locally connected