The Dictionary.com definition of Monopoly serves well: "Exclusive control of a commodity or service in a particular market, or a control that makes possible the manipulation of prices."
Okay, so if you had a company that invented a great new product, like a smoke detector for instance, and wanted to sell it for cost because they wanted to do something good for mankind, in your world they would be broken-up because their very low price would cause them to control that market.