View/manipulate mount namespaces in Linux

Yes. You can look at its /proc/$PID/mountinfo or else you can use the findmnt -N switch - about which findmnt --help says:

• -N, --task <tid>
  • use alternative namespace (/proc/<tid>/mountinfo file)

findmnt also tracks the PROPAGATION flag which is a mountinfo field which reports on exactly this information - which processes share which mounts.

Also, you can always nsenter any type of namespace you like - provided you have the correct permissions, of course.

 nsenter --help
Usage:
 nsenter [options] <program> [args...]

Options:
 -t, --target <pid>     target process to get namespaces from
 -m, --mount [=<file>]  enter mount namespace
 -u, --uts   [=<file>]  enter UTS namespace (hostname etc)
 -i, --ipc   [=<file>]  enter System V IPC namespace
 -n, --net   [=<file>]  enter network namespace
 -p, --pid   [=<file>]  enter pid namespace
 -U, --user  [=<file>]  enter user namespace
 -S, --setuid <uid>     set uid in user namespace
 -G, --setgid <gid>     set gid in user namespace
 -r, --root  [=<dir>]   set the root directory
 -w, --wd    [=<dir>]   set the working directory
 -F, --no-fork          do not fork before exec'ing <program>

 -h, --help     display this help and exit
 -V, --version  output version information and exit

For more details see nsenter(1).