What does "near the city" actually mean in Civilization V?

A lot of buildings in Civilization V mention that they are affected by tiles or resources "near the city", but this quality of being "near a city" is poorly-defined within the game. So what exactly does it mean? I haven't seen any in-depth articles about this topic on the web or in the game's Civilopedia, so I thought I'd outline the important bits here.

Basically, a tile is "near" a city if that city was the first city in its respective empire to claim that tile within its workable radius.

So if you have a single tile or resource that lies between two cities, and both cities' workable ranges overlap that same tile, then that tile is not "near" both cities. It is only "near" the first city that owned that tile. This means that if you go into the city management screen and assign the second city to work that tile, it may receive yield bonuses associated with any improvements or buildings that affect it (such as the stable buffing pasture resources), but the tile's contents will not be considered "near" that second city for other purposes. This includes:

• requirement of an improved Horse or Ivory to build a Circus,
• requirement of an improved Horse, Cow, or Sheep to build a Stable,
• requirement of an improved Iron to build a Forge,
• requirement of an improved Stone or Marble to build a Stone Works,
• requirement of an improved Gold or Silver to build a Mint,
• wonder production bonus from nearby Marble,
• requirement that the city be adjacent to a Mountain in order to build an Observatory,
• trade route income from resource diversity,
• and so on...

Say you have two cities (for example Rome and Antium) whose workable ranges overlap a pastured Horse. Rome was the first city to claim the Horse tile. Rome can, therefore, build a Circus (assuming Trapping has been researched). If you go to the management screen of Antium, you can assign it to work the Horse tile (which prevents Rome from being able to work that tile), but Antium still cannot build a Circus. That is, two cities cannot build a building that requires they both have the same tile.

[LEFT] Rome has annexed a tile containing horses and is building a Circus.
[RIGHT] Later, that tile overlaps with Antium's workable radius, but it cannot build a Circus because the horse was originally claimed by Rome.

Alternatively, if a resource is claimed by a city's culture, but is outside of a city's workable radius (four tiles or more away), then it never counts as "near" that city...