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Page "Compact space" ¶ 14
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single and compact
There are also cycling specific multi-tools that combine many of these implements into a single compact device.
* Any locally compact Hausdorff space can be turned into a compact space by adding a single point to it, by means of Alexandroff one-point compactification.
It is possible to turn the real line into a compact space by adding a single " point at infinity " which we will denote by ∞.
It was possible to predict the number of bases stacked within a single turn of the DNA helix ( 10 per turn ; a full turn of the helix is 27 angströms in the compact A form, 34 angströms in the wetter B form ).
This allowed an engine and boiler to be combined into a single unit compact enough to be used on mobile road and rail locomotives and steam boats.
Since MUMPS allows commands to be strung together on the same line, and since commands can be abbreviated to a single letter, this routine could be made more compact:
In Four Black Dragons various peasants describe the arrival of the American ships with escalating panic, until finally the nightmarish event does seem to be, as claimed, the end of the world .... Someone in a Tree, is a compact Rashomon-and as fine as anything Mr. Sondheim has written ... The single Act II triumph, Bowler Hat, could well be a V. S. Naipaul tale set to music and illustrated with spare Japanese brushstrokes ... Bowler Hat delivers the point of Pacific Overtures so artfully that the rest of Act II seems superfluous.
The # 1 has always been sought after by shooters who appreciate the compact size of a single shot rifle, and the falling block action cuts about four inches off the length of the rifle for a given barrel length.
In the original VHS format, audio was recorded as baseband in a single linear track, at the upper edge of the tape, similar to how an audio compact cassette operates.
In mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact.
Then the Alexandroff extension of X is a certain compact space X * together with an open embedding c: X → X * such that the complement of X in X * consists of a single point, typically denoted ∞.
The ploegg or East Frisian rott was a compact holding that originated with a single lineage or kinship, whose men in early times went to war under their chief, and devolved in medieval times into a union of neighbors rather than kith and kin.
It was reissued on a single compact disc by BMG in 1997 and again by Buddah Records in 2000.
A single sculling oar with an oarlock on the rear transom can be a compact emergency oar.
A non-album Hayward-Lodge song cut at these sessions, " Highway ", was included on the " Say it With Love " twelve-inch single and on a later box set, while the vinyl album did not include their song " Once is Enough " as on the compact disc version.
and Mesopotamia, the latter of which had been remixed, were combined and released together on a single compact disc.
For a few compact ' narrow angle ' V engines, such as the Volkswagen VR6, the angle between the cylinder banks is so narrow that it uses a single head spanning the two banks.
The Chauchat combined a pistol grip, an in-line stock, a large-capacity detachable magazine, and selective-fire capability in a compact package of manageable weight ( 20 pounds ) for a single soldier.
Although tape and other technical advances dramatically improved audio quality of commercial recordings in the post-war years, the basic constraints of the electro-mechanical mastering process remained, and the inherent physical limitations of the main commercial recording media — the 78 rpm disc and the later 7-inch 45 rpm single and the 33-1 / 3 rpm LP record — meant that the audio quality, dynamic range, and running time of master discs were still limited compared to later media such as the compact disc.
A masticating juicer uses a single auger to compact and crush produce into smaller sections before squeezing out its juice along a static screen while the pulp is expelled through a separate outlet.
The same molecular mass was determined, and the presence of a spreading boundary suggested that it was a single compact particle.
Now that advances in compact disc player technology have made the CD acceptable for mixing and " turntablism ", the term maxi single is increasingly used.
By comparison, the " transistor " could fit in a pocket and weighed half a pound, or less, and was powered by standard flashlight batteries or a single compact 9-volt battery.

single and set
A biting, pithy parable of the all-pervading hollowness of modern life, the piece has been set by Mlle Lagoon to a sumptuous score ( a single motif played over and over by four thousand French horns ) by existentialist hot-shot Jean-Paul Sartre.
In order to be able to properly relate the data for a single company each of the three cards comprising the set for each firm was identified with the appropriate serial number of the respondent.
In the center of the tablet is a set of 5 parallel lines equally divided by a vertical line, capped with a semicircle at the intersection of the bottom-most horizontal line and the single vertical line.
By the 27th century BC Egyptian writing had a set of some 24 hieroglyphs which are called uniliterals, to represent syllables that begin with a single consonant of their language, plus a vowel ( or no vowel ) to be supplied by the native speaker.
For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.
In phonology, an allophone (; from the, állos, " other " and φωνή, phōnē, " voice, sound ") is one of a set of multiple possible spoken sounds ( or phones ) used to pronounce a single phoneme.
Typical examples of binary operations are the addition (+) and multiplication (×) of numbers and matrices as well as composition of functions on a single set.
The problem of deciding whether a set of Horn clauses is satisfiable is in P. This problem can indeed be solved by a single step of the Unit propagation, which produces the single minimal model of the set of Horn clauses ( w. r. t.
Because the instructions can be carried out in different types of computers, a single set of source instructions converts to machine instructions according to the central processing unit type.
Whereas a scalar CPU must complete the entire process of fetching, decoding, and executing each instruction and value in a set of data, a vector CPU can perform a single operation on a comparatively large set of data with one instruction.
When these principles are written down into a single collection or set of legal documents, those documents may be said to comprise a written constitution.
A set of ontological distinctions related by a single conceptual metaphor was called an ontological metaphor by George Lakoff and Mark Johnson, who claimed that such metaphors arising from experience were more basic than any properties or symbol-based comparisons.
Since over the course of any single dance, individuals interact with not just their partners but everyone else in the set, contra dancing might be considered a group activity.
Both micro and macroeconomics work together to form a single set of evolving rules and regulations.
The standard works are printed and distributed by the LDS Church in a single binding called a quadruple combination and as a set of two books, with the Bible in one binding, and the other three books in a second binding called a triple combination.
Instead of listing every single element, sometimes an ellipsis ("...") is used, if the writer believes that the reader can easily guess what is missing ; for example, presumably denotes the set of integers from 1 to 100.
What we have done here is arranged the integers and the odd integers into a one-to-one correspondence ( or bijection ), which is a function that maps between two sets such that each element of each set corresponds to a single element in the other set.
A function from the set of real numbers to the real numbers can be represented by a graph in the Cartesian plane ; the function is continuous if, roughly speaking, the graph is a single unbroken curve with no " holes " or " jumps ".

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