  There is a concept in digital topology of a shy map. We define an analogous
concept for topological spaces: We say a function is shy if it is continuous
and the inverse image of every path-connected subset of its image is
path-connected. Some basic properties of such maps are presented. For example,
every shy map onto a semilocally simply connected space induces a surjection of
fundamental groups (but a shy map onto a space that is not semilocally simply
connected need not do so).
