A pure monopoly is characterized by the presence of only one firm in the market, which means there is no competition. Additionally, there are significant barriers to entry by other firms, making it difficult for new players to enter the market. Furthermore, there is a lack of substitute goods for the monopolist's good, meaning consumers do not have alternative options. Lastly, the monopolist has the power to set the price for its product, making it a price-maker. Therefore, all of the given characteristics are true for a pure monopoly.