Where do you store bottles of olive oil that have been opened??

Is it all right to store your half used bottles of olive oil in the refrigerator as opposed to leaving it on a shelf in a cupboard? I know this seems like a small thing but the oil just doesn't seem like it's going to stay fresh for days at room temperature. I've been taking 2 tablespoons of olive oil daily along with 1 teaspoon of Epsom Salts daily. I also drink 3 quarts of fresh squeezed lemonade (no added sugar) daily. I would appreciate any response to the olive oil storage question.

P.S. I rather new to all this.
Thanks

Don