What is the ruling on women performing prayers in a public place?

The Messenger of Allah (peace be upon him) preferred a woman's prayer in her home and made its reward better than her prayer in the mosque. This is based on his (peace be upon him) saying: "A woman's prayer in her home is better than her prayer in her chamber, and her prayer in her private room is better than her prayer in her home." It was also narrated that Umm Humayd built a mosque in the farthest part of her house to pray in. The reason their prayer in homes is better is for safety from fitna (temptation/strife), especially after the emergence of tabarruj (display of adornment) and ostentation. A woman must take precautions when praying in public places and avoid men seeing her. She should not pray in these places except out of necessity and if there is no other place, and with proper covering. As for the saying of some common people that a woman's prayer becomes invalid merely by men seeing her, it has no basis in Islamic law.