Ü (Tibetan: དབུས་, Wylie: dbus, ZYPY: Wü ; pronounced w-yu, similar to English word "we") is a geographic division and a historical region in Tibet. Together with Tsang (Tib. གཙང་, gtsang), it forms Central Tibet Ü-Tsang (Tib. དབུས་གཙང་, Wyl. dbus gtsang), which is one of the three Tibetan regions or cholka (cholka-sum). The other two cholka are Kham (Tib. ཁམས་, Wyl. khams) (Dotod) and Amdo (Tib. ཨ༌མདོ;Wyl. a mdo) (Domed). According to a Tibetan saying, "the best religion comes from Ü-Tsang, the best men from Kham, and the best horses from Amdo".

Constituent districts

Taken together, Ü and Tsang are considered to be the center of Tibetan civilization, from historical, cultural, political and economic perspectives. They are centered on the valley of the Yarlung Tsangpo River, which flows eastward at about 3,600 metres (11,800 ft) above sea level. Of this territory, Ü constitutes the eastern portion, up to Sokla Kyao in the east where it borders to Kham. It includes the Lhasa River valley system, where Lhasa is situated, and the Yarlung and Chonggye valleys to the south of the Tsangpo.

The province of Quebec, Canada, is officially divided into 17 administrative regions. Traditionally (and unofficially), it is divided into around twenty regions. As of the 2011 Canadian Census, the population of Quebec was 7,903,001, the land area was 1,356,547.02 km² and the population density was 5.8 inhabitants per square kilometre.

Administrative

Administrative regions are used to organize the delivery of provincial government services. They are also the basis of organization for regional conferences of elected officers (French: conférences régionales des élus, CRÉ), with the exception of the Montérégie and Nord-du-Québec regions, which each have three CRÉs or equivalent bodies. (In the Nord-du-Québec region, the Kativik Regional Government and Cree Regional Authority, in addition to their other functions, play the role of a CRÉ).

List

The subregions of Montérégie and Nord-du-Québec have their own regional conference of elected officers (CRÉ). Municipalities with 20,000-plus populations in the 2011 Census are listed, with those 50,000 or over bolded. In addition, the seat of the relevant CRÉ is indicated, as well as other major cities and towns. If the population of a CRÉ is less than 20,000, it is shown in italics.

In mathematical analysis, the word region usually refers to a subset of or that is open (in the standard Euclidean topology), connected and non-empty. A closed region is sometimes defined to be the closure of a region.

Regions and closed regions are often used as domains of functions or differential equations.

According to Kreyszig,

According to Yue Kuen Kwok,

See also

Notes and references