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Topology of the United States.

At a gross resolution, just considering the land area, the United States has three disconnected parts:

  • {Alaska, Hawai'i, mainland}.

The complement of the United States is a connected space with a genus of three.

At a finer resolution you would measure a much higher genus. (Does Lake Tahoe count as a “hole” in the mainland US? What about Lake Winnibigoshish?) The Aleutian islands would all register as separate from Alaska, as would the parts of Hawai’i and even Nantucket. So at a fine resolution the complement of the land area of the United States would have a genus well over 100.

http://upload.wikimedia.org/wikipedia/commons/b/b5/Hebridesmap.png

For the UK & Ireland, again it depends on resolution. At a gross scale we could simply talk about two islands but that would leave off Orkney, Man, Guernsey, Jersey, the Hebrides, Skelligs, Ione, Skye, Shetlands, and many more.

http://upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Wfm_shetland_map.png/780px-Wfm_shetland_map.png

According to various Ordnance Surveyors in the Daily Mail (1995):

  • Our 1:625,000 scale database shows Great Britain (England, Scotland and Wales) has a total 6,289 islands, mostly in Scotland. Of these, 803 are large enough to have been ‘digitised’ with a coastline by our map-makers. The rest are recorded as point features
  • The 1:250,000 scale map of Northern Ireland shows 160 islands; 57 offshore.
  • Our 1:250,000 map of the Republic of Ireland has 279 offshore islands.

So, at fine resolution, the genus of the complement

  • |∁ {UK}∪{Ireland}| = 6289

and at a coarser scale, the genus of the complement of the isles is 803.

(Source: Wikipedia)







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