A cat is possible... altough it's better if they go outside sometimes, many people lock them up in their houses. But you have to make some room for the cat. A pillow, or something else soft where he can sleep, a few toys (so he doesn't ruin your stuff), a thing to scratch his nails and a "cat bathroom".

All these things can take up a lot of space in a tiny apartment.

And if you live there alone and have to go to work... he will be alone way too much.

A fish, hamster, lizzard, turtle or bird would be a better idea.