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is and bounded
This theorem is similar to the theorem of Kakutani that there exists a circumscribing cube around any closed, bounded convex set in Af.
This is true of all components which have such a bounded support.
The tract is bounded by Island Ave., Dicks Ave., 61st St., and Eastwick Ave..
The Atlantic Ocean is bounded on the west by North and South America.
** A uniform space is compact if and only if it is complete and totally bounded.
The region is bounded by the Black Sea to the north, the Mediterranean Sea to the south and the Aegean Sea to the west.
The Anatolian peninsula, also called Asia Minor, is bounded by the Black Sea to the north, the Mediterranean Sea to the south, the Aegean Sea to the west, and the Sea of Marmara to the northwest, which separates Anatolia from Thrace in Europe.
Under this definition, Anatolia is bounded to the East by the Armenian Highland, and the Euphrates before that river bends to the southeast to enter Mesopotamia.
To the southeast, it is bounded by the ranges that separate it from the Orontes valley in Greater Syria and the Mesopotamian plain.
thus, as T decreases, ΔG and ΔH approach each other ( so long as ΔS is bounded ).
We now consider how the choice of description language affects the value of K, and show that the effect of changing the description language is bounded.
The South African plateau, as far as about 12 ° S, is bounded east, west and south by bands of high ground which fall steeply to the coasts.
It lies on Abadan Island ( long, 3 – 19 km or 2 – 12 miles wide, the island is bounded in the west by the Arvand waterway and to the east by the Bahmanshir outlet of the Karun River ), from the Persian Gulf, near the Iraqi-Iran border.
The ACT is bounded by the Goulburn-Cooma railway line in the east, the watershed of Naas Creek in the south, the watershed of the Cotter River in the west, and the watershed of the Molonglo River in the north-east.
The Arabian Sea ( Persian Sea ) is a region of the Indian Ocean bounded on on the north by Pakistan and Iran, on the south by northeastern Somalia, on the east by India and on the west by the Arabian Peninsula.
However, the recursion is bounded because in each recursive application either m decreases, or m remains the same and n decreases.
It is bounded by the Scandinavian Peninsula, the mainland of Europe, and the Danish islands.
The Black Sea is bounded by Europe, Anatolia and the Caucasus and is ultimately connected to the Atlantic Ocean via the Mediterranean and the Aegean Seas and various straits.
Since Bulgarian lev is anyway bounded to Euro Bulgaria is looking for more positive outcomes of the becoming a member of the Eurozone rather than risks.
In general, a linear mapping on a normed space is continuous if and only if it is bounded on the closed unit ball.
Note that the requirement that the maps be continuous is essential ; if X is infinite-dimensional, there exist linear maps which are not continuous, and therefore not bounded.

is and east
The point is at a latitude **yl, and the platform is at an error in heading east.
`` Mr. Wycoff's car is waiting for you at the east entrance ''.
It is bordered by Tennessee to the north, Georgia to the east, Florida and the Gulf of Mexico to the south, and Mississippi to the west.
It is situated in the northwest extremity of the North American continent, with Canada to the east, the Arctic Ocean to the north, and the Pacific Ocean to the west and south, with Russia further west across the Bering Strait.
It is a peninsula bound by the Black Sea to the north, Georgia to the north-east, the Armenian Highland to the east, Mesopotamia to the south-east, the Mediterranean Sea to the south, and the Aegean Sea to the west.
It is bordered by Pakistan in the south and the east, Iran in the west, Turkmenistan, Uzbekistan and Tajikistan in the north, and China in the far northeast.
** Eunectes murinus, the green anaconda, the largest species, is found east of the Andes in Colombia, Venezuela, the Guianas, Ecuador, Peru, Bolivia, Brazil and on the island of Trinidad.
The sea's maximum depth is, east of Crete.
Anatolia ( from Greek — " east " or "( sun ) rise "; also Asia Minor, from " small Asia "; in modern ) is a geographic and historical term denoting the westernmost protrusion of Asia, comprising the majority of the Republic of Turkey.
Traditionally, Anatolia is considered to extend in the east to a line between the Gulf of Iskenderun and the Black Sea, approximately corresponding to the western two-thirds of the Asian part of Turkey.
Traditionally, Anatolia is considered to extend in the east to an indefinite line running from the Gulf of Iskenderun to the Black Sea, coterminous with the Anatolian Plateau.
A central massif composed of uplifted blocks and downfolded troughs, covered by recent deposits and giving the appearance of a plateau with rough terrain, is wedged between two folded mountain ranges that converge in the east.
Kildamhnait on the south east coast of Achill is named after St. Damhnait, or Dymphna, who founded a church there in the 16th century.
* 1842 – The Webster – Ashburton Treaty is signed, establishing the Canada – United States border east of the Rocky Mountains.
Armenia is a landlocked country in the Transcaucasia region, between the Black and Caspian Seas, bordered on the north and east by Georgia and Azerbaijan and on the south and west by Iran and Turkey.
Armenia is bordered on the north by Georgia, on the east by Azerbaijan, on the southwest by the Nakhchivan Republic of Azerbaijan, on the south by Iran, and on the west by Turkey.
It is situated between the Black Sea and the Caspian Sea, bordered on the north and east by Georgia and Azerbaijan and on the south and west by Iran and Turkey.
The most common is Martin Waldseemüller's deriving it from Americus Vespucius, the Latinised version of Amerigo Vespucci's name, the Italian merchant and cartographer who explored South America's east coast and the Caribbean sea in the early 16th century.
In the remainder of this region, the southern portion, the most prominent feature is Little Mountain, extending about from east to west between two valleys, and rising precipitously on the north side above them or above the sea.
The Black Warrior River is a considerable stream which joins the Tombigbee from the east.
Abensberg () is a town in the Lower Bavarian district of Kelheim, in Bavaria, Germany, lying around 30 km southwest of Regensburg, 40 km east of Ingolstadt, 50 northwest of Landshut and 100 km north of Munich.
West of Markovo it is in the Anadyr Highlands ( moderate mountains and valleys with a few trees ) and east of Markovo it moves into the Anadyr lowlands ( very flat treeless tundra with lakes and bogs ).
Acapulco ’ s most historic building is the San Diego Fort, located east of the main square and originally built in 1616 to protect the city from pirate attacks.
In the initial stanzas of the poem Asagarth is the capital of Asaland, a section of Asia to the east of the Tana-kvísl or Vana-Kvísl river ( kvísl is " fork "), which Snorri explains is the Tanais, or Don River, flowing into the Black Sea.

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