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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 its
And all the time, she had the heat of hatred in her, like charcoal that is burning on its under side, but not visibly.
There was a measure of protection in its concrete walls and ceiling, but the engineers who hastily installed it were well aware that concrete is not much better than prayer, if as efficacious, when a direct hit comes along.
The long-settled areas of states like Virginia and South Carolina developed the ante-bellum culture to its richest flowering, and there the memory is more precious, and the consciousness of loss the greater.
As it is, they consider that the North is now reaping the fruits of excess egalitarianism, that in spite of its high standard of living the `` American way '' has been proved inferior to the English and Scandinavian ways, although they disapprove of the socialistic features of the latter.
Reduced to its simplest terms, it is an assumption of a collective duty to compensate for the inability of individuals to cope with the rigors of the era.
It is one of the ironic quirks of history that the viability and usefulness of nationalism and the territorial state are rapidly dissipating at precisely the time that the nation-state attained its highest number ( approximately 100 ).
While sovereignty has roots in antiquity, in its present usage it is essentially modern.
There is unceasing pressure, but its sources are immediate.
Others are confined to vast reservations, and not only does the Australian government justifiably not wish them to be viewed as exhibits in a zoo, but on their reservations they are extremely fugitive, shunning camps, coming together only for corroborees at which their strange culture comes to its highest pitch -- which is very low indeed.
But the South is, and has been for the past century, engaged in a wide-sweeping urbanization which, oddly enough, is not reflected in its literature.
All but the most rabid of Confederate flag wavers admit that the Old Southern tradition is defunct in actuality and sigh that its passing was accompanied by the disappearance of many genteel and aristocratic traditions of the reputedly languid ante-bellum way of life.
The answers derived by these means may determine not only the temporal organization of the dance but also its spatial design, special slips designating the location on the stage where the movement is to be performed.
The other variables include the dancer who is to perform the movement and the length of time he is to take in its performance.
Most of these, with horrible exceptions, were conceived as is a ship, not as an attempt to quell the ocean of mankind, nor to deny its force, but as a means to survive and enjoy it.
Hemingway's fiction is supported by a `` moral '' backbone and in its search for ultimate meaning hints at a religious dimension.
In addition, they have been converted to Zen Buddhism, with its glorification of all that is `` natural '' and mysteriously alive, the sense that everything in the world is flowing.
Jazz is good not only because it promotes wholeness but because of its decided sexual effect.
This confession serves to make clear in part what is behind this sexual revolution: the craving for sensation for its own sake, the need for change, for new experiences.
What one actually remembers is its greenness.
the mill-pond is quiet, its surface dark and shadowed, and there does not seem to be much water in it.
But the highroad, according to the description of its traffic, belongs to life as it is lived in unawareness of death, while the way to the churchyard belongs to some other sort of life: a suffering form, an existence wholly comprised in the awareness of death.

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