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Page "Compact space" ¶ 32
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Note and sets
Note where the sun rises and sets, and ask which direction the prevailing winds and storms come from.
Note that the set-theoretic union, in some contexts closely related to logical disjunction ( or ), is used here for sets of statements in such a way that it is more related to logical conjunction ( and ).
Note that the latest version of the syslog protocol draft under development within the IETF includes a mapping between these two different sets of severities.
Note the difference in the front resonator sets of the two vibraphones.
The Julia set of a function ƒ is commonly denoted J ( ƒ ), and the Fatou set is denoted F ( ƒ ).< ref > Note that for other areas of mathematics the notation can also represent the Jacobian matrix of a real valued mapping between smooth manifolds .</ ref > These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century.
Note the fact that the set of points mapped into any hyperplane can be quite convoluted as a result, allowing much more complex discrimination between sets which are not convex at all in the original space.
Note that one formulation of AC is that the Cartesian product of a family of nonempty sets is nonempty ; but since the empty set is most certainly compact, the proof cannot proceed along such straightforward lines.
The labels newly under the Blue Note umbrella are Angel Records, EMI Classics and Virgin Classics ( classical music ), Narada Productions ( contemporary jazz and world-influenced music, including exclusively licensed sub-label Real World Records ), Back Porch Records ( folk and Americana ), Higher Octave Records ( smooth jazz and New Age music ), and Mosaic Records ( devoted exclusively to reissuing jazz recordings in limited-edition boxed sets ).
Note that the set of formulas which define real numbers may exist, as a set F ; the limitation of ZFC is that there is no formula which defines F without reference to other sets.
Note that elements of the Cantor space can be identified with sets of integers and elements of the Baire space with functions from integers to integers.
Note that while both the elements of the Cantor space ( regarded as sets of integers ) and subsets of the Cantor space are classified in arithmetic hierarchies but these are not the same hierarchy.
Note that the boldface hierarchy is just the standard hierarchy of Borel sets.
Note however that several different sets of structure coefficients can give rise to isomorphic algebras.
* Note that the space of rational numbers with the usual topology inherited from the reals is not a Baire space, since it is the union of countably many closed sets without interior, the singletons.
Note that modern set-theoretic definitions usually define operations as maps between sets, so adding closure to a structure as an axiom is superfluous, though it still makes sense to ask whether subsets are closed.
Note that for DNS use, the domain name string is assumed to have been normalized using Nameprep and ( for top-level domains ) filtered against an officially registered language table before being punycoded, and that the DNS protocol sets limits on the acceptable lengths of the output Punycode string.
( Note: Chang and Lendl played a similar match in a semifinal of the 1991 Grand Slam Cup, where Chang again came back from two sets down and won 2 – 6, 4 – 6, 6 – 4, 7 – 6, 9 – 7.
Note that an individual instance of the sentence, such as " Alice, Bob and Carol admire only one another ", need not involve sets and is equivalent to the conjunction of the following first-order sentences:
* Keith Jarrett at the Blue Note ( June 1994 ; live recording ), a six-disc boxed set that documents three nights ( six sets ) in the famous New York City nightclub
Note that a topology τ is stronger than a topology σ ( is a finer topology ) if τ contains all the open sets of σ.
Note that and are closed sets that cannot be separated by open sets, showing that is not normal.
Note the Lamb of God and the twelve sets of figures, gates, and stones.
Note that the symmetric difference of two distinct sets can have measure zero ; hence the pseudometric as defined above need not to be a true metric.

Note and are
( Note: So far as State Police cars are concerned, only their replacement is under this division ).
( Note how strongly the upper lats and serratus are worked in this fine exercise because of the pin-point concentration of force which the dumbbell variation affords ).
( Note: Because of light leakage from one ultraviolet source to another, the lights are switched by a commutator-like assembly rotated by a synchronous motor.
Note that there are 3 trials of interest.
Quite other feelings are evidenced by this style: Af Note the drop to pitch 1 ( the lowest ) on mother with no rise at the end of the sentence ; ;
Note that the scripts mentioned above are not considered proper alphabets, as they all lack characters representing vowels.
( Note that by designating cardinal directions for 1 ,-1,, and, complex numbers such as are considered constructible.
Examples of algebraic integers are,, and ( Note, therefore, that the algebraic integers constitute a proper superset of the integers, as the latter are the roots of monic polynomials for all
Note, however, that the fifth article did not completely deny perseverance of the saints ; Arminius, himself, said that " I never taught that a true believer can … fall away from the faith … yet I will not conceal, that there are passages of Scripture which seem to me to wear this aspect ; and those answers to them which I have been permitted to see, are not of such as kind as to approve themselves on all points to my understanding.
* Note that most ancient Roman sources are quite critical of Agrippina the Younger, because she was seen as stepping outside the conservative Roman ideals regarding the roles of women in society.
Note that this is not the same as a monophyly in which all descendants of a common ancestor are included.
Note: because Solar System bodies are never perfect diffuse reflectors, astronomers use empirically derived relationships to predict apparent magnitudes when accuracy is required.
Note that the 64x16 TRS-80 mode screen uses only a small part of the monitor screen, because the letters are the same size as the 80 × 25 CP / M screen, this was one of the things that was soon after fixed with the redesign to a commercial product
Note that it is often rational to improve a system in an order that is " non-optimal " in this sense, given that some improvements are more difficult or consuming of development time than others.
Note, however, that many municipal bonds are callable, and that this imposes substantial additional risks to the strategy.
Note: This table represents active equipment only ; there are large numbers of equipment in reserve status.
Note however that both in algebra and model theory the binary operations considered are defined on all of S × S.
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.
Note: Concentrations of Cr ( VI ) in US municipal drinking water supplies reported by EWG are within likely, natural background levels for the areas tested and not necessarily indicative of industrial pollution ( CalEPA Fact Sheet ), as asserted by EWG.
Note that arrows between categories are called functors, subject to specific defining commutativity conditions ; moreover, categorical diagrams and sequences can be defined as functors ( viz.
Note that although the carbonate salts of most metals are insoluble in water, the same is not true of the bicarbonate salts.
Note the position of the hydroxyl group ( red or green ) on the anomeric carbon relative to the CH < sub > 2 </ sub > OH group bound to carbon 5: they are either on the opposite sides ( α ), or the same side ( β ).

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