This is a very interesting question. I would agree that education is an important factor in success, but I would not go as far as to say that this fact makes it into a "woman's world." There are several reasons for this.
First, education is open to men and women. So, women do not have a monopoly on education. From this perspective there is a level playing field. To add to this, we can even say that the admittance of women to major colleges was something that took place fairly recently. Columbia University became co-ed in 1981. So, if anything, men still have the advantage.
Second, sexism in the workplaces still exists. According to statistics, men usually still make more than women. From this perspective, men still have an easier time.
In light of two points, the idea of a "women's world" is not tenable when it comes to education and success.