The range sets of continuous functions from [0, 1] into a complete separate metric space are closed, connected, compact, and bounded. The classification of these properties in reverse mathematics has not yet been fully explored prior to this work. Over \(\mathsf{{RCA}}_0\) , the existence of closed set codes for the range sets of continuous functions is equivalent to \(\textsf{WKL}_0\) . The connectedness property is provable in \(\mathsf{{RCA}}_0\) and the compactness and boundedness properties are equivalent to \(\textsf{WKL}_0\) , as long as these properties are carefully defined to avoid the use of a closed code of \(\textsf{range}(f)\) .