Is there a name for a "continuous space of sequences" in the following sense?
i.e. let $f:X\mapsto X$ be a continuous surjective but not necessarily injective function over some compact toplogical space $X$.
Then let $x_{n+1}=f(x_n)$ define some sequence $S_{x0}=(x_0,x_1,x_2,\ldots)$
Then there is a clear sense in which these sequences $S_{x}$ are continuous in the space $X$. How is this concept of a continuous sequence space described or named? I've previously encountered phrases fibre bundle and sheaf which may be related but reading the definitions I'm struggling to tell if either of these is the appropriate concept or where else to look.