** Abstract: **The traditional epsilon-delta definition
of a limit is for functions in metric spaces. This paper
defines limits for relation in topological spaces, and agrees with the
usual definition in the original cases. The advantage is
that less information is needed and more interesting cases are covered,
as the functional dependence on a "variable" is unnecessary for
evaluating the limits of many expressions (for example, the limit of a
Riemann sum as the norm of its partition approaches zero: the relation
between the norm and the sum is not functional, yet the limit is
naturally defined). The general definition is in some ways
simpler, providing enlightening perspectives on traditional uses of
limits, and a context for the generalization of limit extrema (limsup
and liminf) in unordered spaces via a concept of "limit closure."