When I was about 12 years old, about 30 years ago, I used to read and re-read a science fiction short stories book. I think it was an American publication but I may be wrong about that.
The cover had multiple images on it. I believe there were some planets and stars and the picture of a woman (small) and maybe a spaceship of some kind (small). It was soft cover and it was quite thin, could not have been more than 100-150 pages, I think. Similar to an Enid Blyton sized-book and thinner. The colored drawing/pictures on the cover were muted and had a rustic-ness to it.
The first story in the book was about how a detective was going to meet a woman in a rocket-launching station and then it turns out she was beautiful and he fell for her. But she had to leave this planet and I think she did something to him before she left; either wiped his memory or took him with her. Obviously, there are some huge gaps in my memory...
I don't remember much about the other stories in the book, except that one of the other stories was about a planet where a bunch of people were caught outside trying to escape these giant creatures with giant pinchers/claws, like lobsters have. And the final line in that story was how they could here the click-clack of the claws coming closer and they knew they were doomed.