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Compactness and more
* Compactness: A cluster must be sufficiently compact that its fifty or more members lie within one “ counting radius ” of the cluster ’ s centre.

Compactness and important
Compactness generalizes many important properties of closed and bounded intervals in the real line ; that is, intervals of the form for real numbers and.

Compactness and many
* Compactness: Since every open set contains all but finitely many points of X, the space X is compact and sequentially compact.

Compactness and theorems
Category: Compactness theorems

Compactness and theorem
* Compactness theorem
# REDIRECT Compactness theorem
* Compactness theorem

Compactness and .
Compactness, when defined in this manner, often allows one to take information that is known locally — in a neighborhood of each point of the space — and to extend it to information that holds globally throughout the space.
Compactness of the surface is of crucial importance.
Compactness may be shown by invoking equicontinuity.

more and general
`` we the People of the United States, in order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common Defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America ''.
He was referring not only to the general college situation but more especially to the preparatory schools.
And it is clearly argued by Lord Percy of Newcastle, in his remarkable long essay, The Heresy Of Democracy, and in a more general way by Voegelin, in his New Science Of Politics, that this same Rousseauan idea, descending through European democracy, is the source of Marx's theory of the dictatorship of the proletariat.
In this essay, we are, along with most historians, interested in the more general or more inclusive ideas, that are so to speak `` writ large '' in history of literature where they recur continually.
An idea, of the sort that we have in mind, although of necessity readily available to imagination, is more general in connotation than most poetic or literary images, especially those appearing in lyric poems that seek to capture a moment of personal experience.
The publication of Father Connolly's The Man Has Wings has made more of the group available in print so that a general picture of what it contained can now be had without difficulty.
But Morgan evidently reported matters of intelligence much more important to his commanding general.
Those who do have occasion to deal with the invasions in a more general way, like T.W. Shore and Arthur Wade-Evans, are on the side of a gradual and often peaceful Germanic penetration into Britain.
One is impressed with the dignity, clarity and beauty of this new translation into contemporary English, and there is no doubt that the meaning of the Bible is more easily understandable to the general reader in contemporary language in the frequently archaic words and phrases of the King James.
On this point there was fairly general agreement that assessors would like to do more than they are doing now.
and ( C ) to finance, for not more than three years beyond the end of said period, such activities as are required to correlate, coordinate, and round out the results of studies and research undertaken pursuant to this Act: Provided, That funds available in any one year for research and development may, subject to the approval of the Secretary of State to assure that such activities are consistent with the foreign policy objectives of the United States, be expended in cooperation with public or private agencies in foreign countries in the development of processes useful to the program in the United States: And provided further, That every such contract or agreement made with any public or private agency in a foreign country shall contain provisions effective to insure that the results or information developed in connection therewith shall be available without cost to the United States for the use of the United States throughout the world and for the use of the general public within the United States.
In general, such apartments afford more protection than smaller buildings because their walls are thick and there is more space.
As I have repeatedly stated, this provision is much more restrictive than the general law, popularly known as the Buy American Act.
For the near term, however, it must be realized that the industrial and commercial market is somewhat more sensitive to general business conditions than is the military market, and for this reason I would expect that any gain in 1961 may be somewhat smaller than those of recent years ; ;
In type 3, this general relationship is maintained peripherally but not centrally where the pulmonary vein follows a more independent path to the hilum as is the case throughout the lung in type 2.
This will be more or less our general method for the second problem.
The theorem which we prove is more general than what we have described, since it works with the primary decomposition of the minimal polynomial, whether or not the primes which enter are all of first degree.
In general, the approach is more active than passive, more out-reaching than reflective.
A more realistic analysis must take into account the fact that Brandywine people in the urban-fringe area are, in general, less segregated locally than group members in rural areas.
All of them felt a compelling need for more coverage on areas that could be only lightly touched upon in a general survey functional course.
Thus, this readiness to relax controls, evidenced in the Kohnstamm situation, appears to be a more general personality factor.
The tendency for general business activity to soften somewhat is becoming more evident.

more and situation
But in our case -- and neither my wife nor I have extreme views on integration, nor are we given to emotional outbursts -- the situation has ruined one or two valued friendships and come close to wrecking several more.
Upon second thought we were forced to realize that we have very few reliable historical benchmarks against which we might compare the present situation, and that conclusions that present-day students are `` more '' or `` less '' religious could not be defended on the basis of our data.
But when the situation was so complicated that even Nogaret, one of the principal actors in the drama, could misinterpret the pope's motives, it is possible that Othon and his companions, equally baffled, attributed their difficulties to a more immediate cause.
But this situation of Kent House was more subtle.
The last thing in the world that resembled a war was our line of farmers and storekeepers and mechanics perched on top of a stone wall, and this dashing rider made us feel a good deal sharper and more alert to the situation.
Action taken today is often far more valuable than action taken several months later in response to a situation then out of control.
Here there is a specific preventive component which applies in a more generalized sense to any casework situation.
A more tenable explanation for the change in reactions is that the added knowledge and increased familiarity with the total situation made it possible for these subjects to be less guarded and to relax, since any reaction seemed acceptable to the examiner as `` normal ''.
He becomes more callous, the population becomes more hostile, the situation grows more tense, and the police force is increased.
There are two more Sunday afternoons when the situation will arise.
Although the theological forms of the past continue to exist in a way they do not in a more secularized situation, the striking thing is the rapidity with which they are being reduced to a marginal existence.
One of the more noteworthy changes that have taken place since the mid-19th century is the situation of Catholics at Oxford and Cambridge Universities.
Besides that, I'm acquainted more or less with the defense hardware situation through my contacts in the Air Force.
This is not the most general situation of a Cartesian product of a family of sets, where a same set can occur more than once as a factor ; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family.
Although he was committed to maintaining what the church had defined at Nicaea, Constantine was also bent on pacifying the situation and eventually became more lenient toward those condemned and exiled at the council.
The situation may become widespread and result in more serious and permanent consequences.
When AI researchers attempt to " scale up " their systems to handle more complicated, real world situations, the programs tend to become excessively brittle without commonsense knowledge or a rudimentary understanding of the situation: they fail as unexpected circumstances outside of its original problem context begin to appear.
It was Capp's finely tuned sense of the absurd, his ability to milk an outrageous situation for every laugh in it and then, impossibly, to squeeze even more laughs from it, that found such favor with the public ," ( from Don Markstein's Toonopedia ).
The water level is generally far more dependent on the regional wind situation than on tidal effects.
In that case, the situation is a little more complicated.
Staff burden was reduced at the top and spread among commands more knowledgeable about their own situation.

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