  It is a well-known fact that every path-connected Hausdorff space is arcwise
connected. Typically, this result is viewed as a consequence of a sequence of
fairly technical results from continuum theory. In this note, we exhibit a
direct and simple proof of this statement, which makes explicit use of Zorn's
Lemma. Additionally, by carefully breaking down the proof, we identify a modest
improvement to a class of spaces relevant to algebraic topology.
