Master of Science
Gulden, Samuel L.
A curve has often been thought of as the "path of acontinuous moving point". This concept of a curve is again associatedd with the intuitive notion of "thinness". However, the path of a continuously moving point is not a thin or curve-like set. To speak more precisely about curves and arcs, we shall employ notions out of point set topology: the notion of a metric space; of compactness; of connectedness; and of ordering.
Hsieh, David Kuo-shu, "Arcs and Peano continua" (1961). Theses and Dissertations. 3055.