a specific case of a monopoly. It's existence is justified by the specific cost structure the monopolist, which barrs other competitors from entering he market by making it impossible for him to produce and sell his goods at a profit. A good practical example is a railway company - a competitor would have to build a second set of tracks in a specific area in order to be able to enter the market. Technically this implicates that the monopolists' long term average costs (LAC?) and long term marginal costs (LMC?) decrease when the output Q increases.
However, I do have an uninformed opinion: I think it is an open matter of discussion whether any "natural" monopolies exist. It is very hard to do experiments on the national or continental scale, so tradition or ideology has determined what gets to be a monopoly. Radio and TV stations were governmental monopolies in most west European democracies for most of the 20th century. Each city has a municipal monopoly for street lights. Each country has a monopoly currency. Some libertarian economists might think we could handle multiple currencies, regulated by private banks, and there would be no need for a central bank. Maybe this uncertainty should be reflected in the definition.
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