Let L be a connected linearly ordered topological space and let f
be a continuous function from L into itself. if P (f) and R(f) denote
the set of periodic points and the set of recurrent points of f respectively,
we show that the center of f is $cl_{L}P(f)$ and the depth of the
center is at most 2. Furthermore we have $cl_{L}P(f)=cl_{L}R(f)$.
