Opposite words for egress:
access, immersion, entryway, entrance, entry, entrée, entranceway, ingress.
Usage samples:
  1. Even in this event, however, a great part of the lubricating material will be lost from finding rapid egress through the opening of the brasses.
    "Modern Machine-Shop Practice, Volumes I and II", Joshua Rose.
  2. Thorndyke picked up his hat, but Matravers barred his egress.
    "Berenice", E. Phillips Oppenheim.
  3. This pressure will be permanent so long as the air has no egress from the cavity of the pleura.
    "Surgical Anatomy", Joseph Maclise.
  4. In the hall Hood intercepted Deering in the act of effecting egress by way of the front door.
    "The Madness of May", Meredith Nicholson.