And no man in heaven - No one - οὐδεὶς oudeis. There is no limitation in the original to man. The idea is, that there was no one in heaven - evidently alluding to the created beings there - who could open the volume. Is it not taught here that angels cannot penetrate the future, and disclose what is to come? Are not their faculties limited in this respect like those of man?
Nor in earth - Among all classes of people - sages, divines, prophets, philosophers - who among those have ever been able to penetrate the future, and disclose what is to come?
Neither under the earth - These divisions compose, in common language, the universe: what is in heaven above; what is on the earth; and whatever there is under the earth - the abodes of the dead. May there not be an allusion here to the supposed science of necromancy, and an assertion that even the dead cannot penetrate the future, and disclose what is to come? Compare the notes on Isaiah 8:19. In all these great realms no one advanced who was qualified to undertake the office of making a disclosure of what the mysterious scroll might contain.
Was able to open the book - Had ability - ἠδύνατε ēdunate - to do it. It was a task beyond their power. Even if anyone had been found who had a rank and a moral character which might have seemed to justify the effort, there was no one who had the power of reading what was recorded respecting coming events.
Neither to look thereon - That is, so to open the seals as to have a view of what was written therein. That it was not beyond their power merely to see the book is apparent from the fact that John himself saw it in the hand of him that sat on the throne; and it is evident also Revelation 5:5 that in that sense the elders saw it. But no one could prevail to inspect the contents, or so have access to the interior of the volume as to be able to see what was written there. It could be seen, indeed Revelation 5:1, that it was written on both sides of the parchment, but what the writing was no one could know.

And no man - Ουδεις· No person or being.
In heaven - Among all the angels of God.
Nor in the earth - No human being.
Neither under the earth - No disembodied spirit, nor any demon. Neither angels, men, nor devils, can fathom the decrees of God.
Neither to look thereon - None can look into it unless it be opened, and none can open it unless the seals be unloosed.

(4) And no man in heaven, nor in earth, neither under the earth, was able to open the book, neither to look thereon.
(4) Thus neither of them that are in heaven, nor of them who are in the earth. Now this counting of parts, is sufficient to the denying of the whole; For of the creatures, one sort is in heaven, above the earth: another in the earth, and another under the earth in the sea, as is later declared in (Revelation 5:13).

And no man in heaven,.... Or "no one in heaven", whether angels, or the souls of departed saints; neither the one nor the other know anything of what is to come, until it is revealed unto them:
nor in earth: among all the men on earth, even those of the greatest sagacity and penetration, the wise, the prudent, the scribe, the disputer of this world, such who are most conversant with books, and have the greatest reach into the things of nature, or of grace:
neither under the earth; the dead buried there, good or bad; which may be said agreeably to the notions of the ancient Jews, who believed the immortality of souls, and that they were rewarded or punished, , "under the earth", according to their virtue or vice in life (d): or the devils in hell; or whoever on the earth are influenced by them, as magicians, sorcerers, soothsayers, and necromancers:
was able to open the book, neither to look thereon; or in it, so as to read it, understand it, and show to John what was in it; for the sense is, there was no creature in heaven, earth, or hell, who were masters of the deepest knowledge, and made pretensions to any, that were able to foresee and foretell things to come; or to exhibit the prophecies in this book, and represent them to John in the manner they afterwards were, and much less to accomplish them.
(d) Joseph. Antiqu. l. 18. c. 1. sect 3.

no man--Greek, "no one." Not merely no man, but also no one of any order of beings.
in earth--Greek, "upon the earth."
under the earth--namely, in Hades.
look thereon--to look upon the contents, so as to read them.

And no one in the heaven, or on the earth . . . was able to open the book. No one (the word man does not occur in the Greek) was found able to open the book, for no one can penetrate the future. It is held in the strong right hand of Him who sits on the throne, the omnipotent disposer of the future, who controls the destiny of churches, men, and nations. The sweep of the panorama, that has pictured forth upon its canvas the destiny of the Church and the world, cannot begin until the seals of this book are opened. Had no one been found able to open the seals, the closing book of the Bible would never have been written.

And none - No creature; no, not Mary herself. In heaven, or in earth, neither under the earth - That is, none in the universe. For these are the three great regions into which the whole creation is divided. Was able to open the book - To declare the counsels of God. Nor to look thereon - So as to understand any part of it.