What I remember:
A man (whose family is dead) purchases a machine that can form metal objects of any shape. The man wants to return the machine for some reason, so he figures he'll try making something impossible. He keys in a "devil's tuning fork," which, to his surprise, it creates. He looks into the impossible space and sees his family. The story ends with him keying in a larger version so he can go through the space to his family.
FYI, a "devil's tuning fork" is the same thing as a blivet, poiuyt, or widget (see wikipedia's blivet article if you need more information)
Also, I do remember some of the other stories from this book, but not as intensely as the above. Here are the details:
In this story people live in houses and get from place to place via walk though teleportation doors. No-one ever goes outside and the lawns and gardens are all looked after by robots. The story focuses on a boy who teleports to school and back, but he is always looking outside, wanting to explore. In the end he does get outside and sees some amazing things.
The other story is about how the world has been converted into a massive junkyard. No animals or plants exist, and only one man is present. He spends his time searching through all the filth, and one day he discovers a lemon seed. He is able to grow this lemon tree, which produces one lemon. He eats the lemon, but dies. The tree was grown in pure garbage, and the lemon is pure poison.
I've been after this for years so anything anyone knows will make my day.