Help


[permalink] [id link]
+
Page "Complete metric space" ¶ 21
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

is and only
Bryn Mawr Drive is only two or three miles from the Spartan, and it took me less than five minutes to get there.
Actually, only two men know what the formula is, Blake and '' -- He stopped and looked at Thor's body.
In fact it has caused us to give serious thought to moving our residence south, because it is not easy for the most objective Southerner to sit calmly by when his host is telling a roomful of people that the only way to deal with Southerners who oppose integration is to send in troops and shoot the bastards down.
This is the only case in modern history of a people of Britannic origin submitting without continued struggle to what they view as foreign domination.
Recognizing that the Rule of Law is `` a dynamic concept which should be employed not only to safeguard the civil and political rights of the individual in a free society '', the Congress asserted that it also included the responsibility `` to establish social, economic, educational and cultural conditions under which his legitimate aspirations and dignity may be realized ''.
It is the gait of the human who must run to live: arms dangling, legs barely swinging over the ground, head hung down and only occasionally swinging up to see the target, a loose motion that is just short of stumbling and yet is wonderfully graceful.
They are huge areas which have been swept by winds for so many centuries that there is no soil left, but only deep bare ridges fifty or sixty yards apart with ravines between them thirty or forty feet deep and the only thing that moves is a scuttling layer of sand.
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.
`` Now that Bruno Walter is virtually in retirement and my dear friend Dimitri Mitropoulos is no longer with us, I am probably the only one -- with the possible exception of Leonard Bernstein -- who has this special affinity for and champions the works of Bruckner and Mahler ''.
Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.
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.
I think it is essential, however, to pinpoint here the difference between the two concepts of sovereignty that went to war in 1861 -- if only to see better how imperative is our need today to clarify completely our far worse confusion on this subject.
To my knowledge, Lincoln remains the only Head of State and Commander-in-Chief who, while fighting a fearful war whose issue was in doubt, proved man enough to say this publicly -- to give his foe the benefit of the fact that in all human truth there is some error, and in all our error, some truth.
It is all around us and our only chance now is to let it in.

is and pseudometric
This turns the seminormed space into a pseudometric space ( notice this is weaker than a metric ) and allows the definition of notions such as continuity and convergence.
* Every metric space is Tychonoff ; every pseudometric space is completely regular.
More generally, every topological space which is homeomorphic to an open subset of a complete pseudometric space is a Baire space.
In mathematics, a pseudometric space is a generalized metric space in which the distance between two distinct points can be zero.
In the same way as every normed space is a metric space, every seminormed space is a pseudometric space.
A pseudometric space is a set together with a non-negative real-valued function ( called a pseudometric ) such that, for every,
Unlike a metric space, points in a pseudometric space need not be distinguishable ; that is, one may have for distinct values.
The pseudometric topology is the topology induced by the open balls
More generally, every topological space which is homeomorphic to an open subset of a complete pseudometric space is a Baire space.
Intuitively, this has the consequence that all points of the space are " lumped together " and cannot be distinguished by topological means ; it belongs to a pseudometric space in which the distance between any two points is zero.

is and yet
The woman eyed the youth with the avidity a coin collector might display toward a rare doubloon which is not yet in his collection.
William Styron, while facing the changing economy with a certain uneasy reluctance, insists he is not to be classified as a Southern writer and yet includes traditional Southern concepts in everything he publishes.
That is why, the argument runs, the squares are so fearful of jazz and yet perversely fascinated by it.
And yet -- a year to a child is an eternity, and in the memory that phase of one's being -- a certain mental landscape -- will seem to have endured without beginning and without end.
And yet amid all the gay hedonism in Pilgrimage And Wander-Years is a cycle of short poems, `` Thoughts In Loneliness '', filled with brooding, melancholy, and sombre longing ''.
But he plunges into yet another, this time with Norway, and is killed in an assault on the fortress of Fredrikshall, being only thirty-six years of age when he died.
Further, change is a form of motion, it occurs as the act of a being in potency insofar as it is in potency and has not yet reached the terminus of the change.
it conceals and yet is suggestive ; ;
William Wimsatt and Cleanth Brooks, it seems to me, have a penetrating insight into the way in which this control is effected: `` For if we say poetry is to talk of beauty and love ( and yet not aim at exciting erotic emotion or even an emotion of Platonic esteem ) and if it is to talk of anger and murder ( and yet not aim at arousing anger and indignation ) -- then it may be that the poetic way of dealing with these emotions will not be any kind of intensification, compounding, or magnification, or any direct assault upon the affections at all.
One is Greece is not yet suffering from overpopulation.
yet the tide is too strong against us, and I fear ( if the framer of hearts help not ) it will force me to little Patience, a little isle next to your Prudence ''.
yet here was a depth of sensibility which is lacking in a considerable portion of the beneficiaries of our civilization.
We may further grant to those of her ( Poetry's ) defenders who are lovers of poetry and yet not poets, the permission to speak in prose on her behalf: let them show not only that she is pleasant but also useful to States and to human life, and we will listen in a kindly spirit ; ;
In spite of the armistice negotiated by Amadee two years earlier, the war between Bishop Guillaume of Lausanne and Louis of Savoy was still going on, and although little is known about it, that little proves that it was yet another phase of the struggle against French expansion and was closely interwoven with the larger conflict.
If it proclaims that the best is yet to be, it always arouses, at least in the young, either a suspicious question or perhaps the exclamation of the Negro youth who saw on a tombstone the inscription, `` I am not dead but sleeping ''.

is and metric
** In metric geometry an automorphism is a self-isometry.
In Riemannian geometry, the metric tensor is used to define the angle between two tangents.
The meter is defined to be a unit of proper length, but the SI definition does not specify the metric tensor to be used in determining it.
There is an active trade in the shells, which sell for more than US $ 1, 400 per metric tonne.
In the metric system, the hectare is commonly used for the same purpose.
1 international acre is equal to the following metric units:
However, a common and well-accepted metric is the half power points ( i. e. frequency where the power goes down by half its peak value ) on the output vs. frequency curve.
The metric for noise performance of a circuit is noise figure or noise factor.
The lowercase letter o for octet is defined as the symbol for octet in IEC 80000-13 and is commonly used in several non-English languages ( e. g., French and Romanian ), and is also used with metric prefixes ( for example, ko and Mo )
It is still used in metric English-speaking countries ( such as Canada ), and remains the standard unit of classification for air conditioning units manufactured and sold in many non-English-speaking metric countries.
Through the work of Werner Israel, Brandon Carter, and David Robinson the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr – Newman metric ; mass, angular momentum, and electric charge.
The most general stationary black hole solution known is the Kerr – Newman metric, which describes a black hole with both charge and angular momentum.
Blood alcohol content ( BAC ), also called blood alcohol concentration, blood ethanol concentration, or blood alcohol level is most commonly used as a metric of alcohol intoxication for legal or medical purposes.
Despite serious terrain obstacles, almost three-quarters of all cross-border dry cargo is now transported by road, 105, 251 metric tons in 2005.
In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.
In fact, every compact metric space is a continuous image of the Cantor set.
Note that, in a metric space, every compact subset is closed and bounded.
* A metric space ( or uniform space ) is compact if and only if it is complete and totally bounded.
* If the metric space X is compact and an open cover of X is given, then there exists a number such that every subset of X of diameter < δ is contained in some member of the cover.

0.095 seconds.