Would the following change address your concerns?
Section 4.1.1., paragraph 3:
OLD:
o The Internet requires a globally unique namespace
NEW:
o The Internet requires a globally unique namespace: a namespace in
which any given name refers to the same information (has the same
meaning) no matter who requests that information and no matter
from which specific name server they request it.
Section 4.1.1., paragraph 4:
OLD:
o Private networks may operate private namespaces, but still require
that names in the public namespace be globally unique.
NEW:
o Private networks may operate private namespaces, with names that
have meanings only locally (within the private network) but still
require that names in the public namespace be globally unique.
This is to the paragraphs preceding the one you commented on, but I think it
does a good job of introducing the concepts used in the paragraphs you
commented on, in a fairly natural way.
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