Is an entirely black umbrella considered for men, and is it permissible for a woman to use it?

The basic principle regarding clothing is permissibility and lawfulness, except for what has been explicitly prohibited. The criterion for forbidden imitation of men is wearing what is customarily and predominantly specific to men, and which women do not ordinarily wear. Thus, anything not specific to men is not forbidden for women to wear. Imitating men is forbidden and is considered one of the major sins.