We examine the existence of
K-to-1 functions f:**R**-->**R** in the class
of continuous functions, Darboux functions, functions
with perfect road, and functions with Cantor intermediate
value properties. In this setting K stands for a cardinal
number (finite or infinite).
We also consider different variations on this theme.

**Requires rae.cls file**
and amsmath.sty

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**Last modified September 10, 1998.**