Is it possible to win culturally in Civilization V with only one city?

I got a cultural victory with India with just my capital. I played on a archipelago map on prince where I had a small land mass all to myself until mid-late game. If I were playing on a higher difficulty I would have been worried about defense. I was falling heavily behind on research and the last 75 turns or so was me spamming next turn.

As it was I didn't win until 2032, so I squeaked it in barely.

Edit: I tried previous to this on a continents map and fell so far behind on research that with four other civs on the continent that I was bullied by England, so I restarted on the archipelago map.

Because with few exceptions, culture is capped to being produced by cities it is generally not effective (though certainly feasible) to win with only one city. The break even points (in terms of when the potential culture gained by a new city equals the increased cost of social policies) varies depending on tech level, map size, and game speed (And whether you have Cristo Redentor).

An easy way around this is to simply use one city and a strong military to puppet most of your neighbors. They puppet-ed cities will provide the city-based culture without increasing the costs of social policies.

From what I understand, 3-4 owned cities is a good number on most standard maps.(and as many cultural city-states as your coffers can keep happy)

The first column is the cost of a new policy with 1-city being set to an index value of 1. The second column is the gain of culture assuming equal production of culture per city. The third is the ratio between the two. Higher is better because you want more producers and less price. And the clean answer is: 4 is the optimal number of cities.

And then, yes yes, you can discuss a lot more on the advantages of adding one or two extra cities because it gives you strategic or monetary advantages that might come in handy. But that's a tactical call in the given situation.