I read a short story in the late 70's or early 80's, but cannot remember the title or the author.
In the story a man opens a door in either a house or room and sees someone in the distance. He goes through a sequence of events where he ends up as that person, effectively stuck in a time-loop forever.
The story was in a book of short stories. When I was younger I thought the story was called 'By his Bootstraps'. I now know that it wasn't that story but it could have been in an anthology with that story.
I cannot remember much about the story except that the man only realised at the end of the story that he had seen himself and would have to keep repeating the sequence in a loop.