1. Julie’s father’s mind was made up not to let her have her own car. She said that he didn’t have an open mind about the matter, and that he had not given her a fair chance to persuade him.
2. I have almost decided to vote for the conservative candidate, but I’m still willing to listen to what the other candidates have to say. I’m trying to keep an open mind about all the candidates until election day.

Antonym: closed-minded. Open-minded and closed-minded generally refer to a person’s overall outlook or approach, whereas keep an open mind is used to describe one’s approach to one particular situation or topic.