Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
$\begingroup$Thanks, Let now $X$ a compact manifold and $p: X^{S^1}\longrightarrow X$ a fibration that admits sections. Set $Sect(p)$ the non empty set of that sections, topologized with the open compact topology. My question is: $Sect(p)$ inherits also a structure of manifold$\endgroup$