diff --git a/man5/core.5 b/man5/core.5
index 096f8152f..f780ce681 100644
--- a/man5/core.5
+++ b/man5/core.5
@@ -210,13 +210,12 @@ is nonzero, then .PID will be appended to the core filename.
 
 Paths are interpreted according to the settings that are active for the
 crashing process.
-That means the current
-.BR mount_namespaces (7),
-the current working directory (found via
+That means the crashing process's mount namespace (see
+.BR mount_namespaces (7)),
+its current working directory (found via
 .BR getcwd (2)),
-and the current
-.BR chroot (2)
-path.
+and its root directory (see
+.BR chroot (2)).
 
 Since version 2.4, Linux has also provided
 a more primitive method of controlling
@@ -252,12 +251,9 @@ and must immediately follow the '|' character.
 .IP *
 The program pathname is interpreted with respect to the initial mount namespace
 as it is always executed there.
-It is not affected by the settings of the crashing process
-(e.g. the process using
-.BR chroot (2)
-or
-.BR mount_namespaces (7)
-or similar modifications).
+It is not affected by the settings
+(e.g., root directory, mount namespace, current working directory)
+of the crashing process.
 .IP *
 The process created to run the program runs as user and group
 .IR root .
@@ -265,16 +261,16 @@ The process created to run the program runs as user and group
 Running as
 .I root
 does not confer any exceptional security bypasses.
-Namely, LSMs (e.g. SELinux) are still active and may prevent the handler
+Namely, LSMs (e.g., SELinux) are still active and may prevent the handler
 from accessing details about the crashed process via
-.I /proc/PID
+.IR /proc/[pid] .
 .IP *
 The process created runs in the initial namespaces (pid, mount, user, etc...)
 and not in the namespaces of the crashing process.
-You can utilize specifiers like
+One can utilize specifiers such as
 .I %P
 to find the right
-.I /proc/PID
+.I /proc/[pid]
 directory and probe/enter the crashing process's namespaces if needed.
 .IP *
 Command-line arguments can be supplied to the