A monopoly need not control the entire market for a product. A monopoly is simply a firm which has enough market power to preclude any meaningful competition. They can act as they wish and charge what they wish without fear that their consumers will turn to competing firms for better products and lower prices. It is worth mentioning that not only can a firm be a monopoly if their market share is a far cry from 100%, but also that being a monopoly is not in itself illegal. In order for a company to be found guilty of antitrust violations, they must have either abused their market power, or went to unfair lengths to maintain their monopoly.