Is it permissible for a woman in mourning to go out to the market to take care of her needs?

It is permissible for the woman in mourning (for her deceased husband) to go out for important needs such as the market, medical treatment, teaching, and seeking knowledge, while avoiding adornment, perfume, and jewelry. She must observe five matters: remaining in the marital home, avoiding beautiful clothes, avoiding perfume (except when purifying from menstruation), not wearing jewelry, and not using kohl or henna.