[permalink] [id link]
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.
from
Wikipedia
Some Related Sentences
Note and requirement
Note also that until well into the 20th Century, rather than an official readying the ball for scrimmage, the side entitled to the snap had complete custody of the ball and could snap it from the required spot at any time ; for instance, a tackled ball carrier might feign injury, then suddenly snap the ball while recumbent, there being no stance requirement yet.
Note that former military officers from the World War II era may be appointed prime minister despite the " civilian " requirement, Yasuhiro Nakasone being one prominent example.
Note that none of these listed characteristics are a requirement, as seen in shōnen manga like Yotsuba &!, which features a female lead, and almost no fan service or action, and that what most defines whether or not a series is shōnen are things like the magazine ( see Weekly Shōnen Jump ) it is serialized in or the time slot it airs on T. V.
Note 2: The FCC registration program contains no requirement that accepted terminal equipment be compatible with, or function with, the network.
Note: Part 68 rules provide the technical and procedural standards under which direct electrical connection of customer-provided telephone equipment, systems, and protective apparatus may be made to the nationwide network without causing harm and without a requirement for protective circuit arrangements in the service-provider networks.
Note that the requirement d ( T ( x ), T ( y )) < d ( x, y ) for all unequal x and y is in general not enough to ensure the existence of a fixed point, as is shown by the map T: < nowiki >
Note that the obvious compatibility condition, namely, that this marginal probability distribution be in the same class as the one derived from the full-blown stochastic process, is not a requirement.
Note that there is no requirement for uniqueness over time.
Note that at least for type specimens there is no requirement for a " typical " individual to be used.
Note that both files have been sorted on the join field — this is a requirement of the program.
Note that this requirement can be rephrased by saying that binary meets preserve binary joins.
Note that using the channel numbers in an identification is not a requirement.
Note that there is no requirement of commutativity.
Note and maps
Note that the axioms are given in terms of the maps ( binary product, unary inverse, and nullary identity ), hence are categorical definitions.
Note that this is stated in terms of maps – product and inverse must be maps in the category – and without any reference to underlying " elements " of group – categories in general do not have elements to their objects.
a function that associates a header with each relation name in R. ( Note that this is a simplification from the full relational model where there is more than one domain and a header is not just a set of column names but also maps these column names to a domain.
Note that Read's Island is the spelling used by the Ordnance Survey and other maps, whilst some spell it Reads Island, and others even Reed's or Reeds Island.
Note that symplectic maps are volume-preserving, orientation-preserving, and are vector space isomorphisms.
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.
* π is nondegenerate, that is the space of vectors π ( x ) ξ is dense as x ranges through A and ξ ranges through H. Note that if A has an identity, nondegeneracy means exactly π is unit-preserving, i. e. π maps the identity of A to the identity operator on H.
Note the very strong and crucial hypothesis that f maps the fundamental class of M to the fundamental class of N. Naturality does not hold for an arbitrary continuous map f, since in general f < sup >∗</ sup > is not an injection on cohomology.
Note: The expressway is shown on maps in Beijing to link directly and seamlessly with the Jingha Expressway.
Note that Queenstown Road station's modern entrance and platform signage lacks the "( Battersea )" suffix that is applied to it on timetables and some maps, i. e. Queenstown Road ( Battersea ).
Note however that during Capture The Flag matches the maps are downsized.
Note the gaslights, chalkboards, moveable walls, and the maps and pictures on the walls
Note that some of these names do not appear on maps, and some alternative names are indicated below.
Note that the Chinese source maps were of " consumer use.
Note that the correct location for the port is as follows, rather than at Aird Mhidhinis as shown on some printed Ordnance Survey maps.
Note: Col. map with 7 ancillary maps.
Note: Col. map with 5 ancillary maps.
Note, however, that a dispute over the location of the boundary between Canada and Labrador ( a dependency of the Dominion of Newfoundland ) meant both Canada and Newfoundland claimed the far eastern portion of Ungava, an area shown in shaded red on the accompanying maps.
Note that the connection coefficients become Möbius transformations on the triangle maps.
Note that both of these maps are practically computable.
Note that, by definition, a retraction maps X onto A.
Note that the compiler inferred the type of this function to be, meaning that this function maps ints onto ints.
Note and be
Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.
Note extent of these interests and how available they will be for the public to enjoy.
Note that we need not know the value of p, for the experiment to be binomial.
Note that the acid can be the charged species and the conjugate base can be neutral in which case the generalized reaction scheme could be written as HA < sup >+</ sup > H < sup >+</ sup > + A.
Most European domestic power supplies run at 230 V, so the current drawn by a particular European appliance ( in Europe ) will be less than for an equivalent American one ( in the United States ).< ref group =" Note "> The formula for power is given by
Note that this premise uses the phrase " is not ", a form of " to be "; this and many other examples show that he did not intend to abandon " to be " as such.
Note that strengthened negations may be compatible with weakened forms of AC.
Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.
Note that the RGB color may be premultiplied, hence saving the additional multiplication before RGB in the equation above.
* In the Star Wars prequels, the galactic capital planet Coruscant has buildings many miles tall, and approaches the completely built-over condition of Trantor in Isaac Asimov's classic Foundation trilogy ( Note: due to this, Coruscant was originally to be named Jhantor but was eventually renamed Coruscant ).
Note that wav files can also be encoded with the gsm codec.
Note that this expression is not well-defined for all time series or processes, because the variance may be zero ( for a constant process ) or infinite.
Note that just because a player is described as being " at bat " in this sense, he will not necessarily be given an at bat in his statistics ; the phrase actually signifies a plate appearance ( assuming it is eventually completed ).
( Note that K is the SI unit for temperature ( kelvin ) and should not be confused with k, the SI prefix for kilo.
Note that this calendar will normally need to add a 53rd week to every 5th or 6th year, which might be added to December or might not be, depending on how the organization uses those dates.
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 this is different from the recursive languages which can be decided by an always-halting Turing machine.
) Note that the same set of points would not have, as an accumulation point, any point of the open unit interval ; hence that space cannot be compact.
Note that the points must all be different numbers for them to count towards the fire bet.
Note that for any fixed w the function f ( x ) = F ( w x ) is computable ; thus the universality property states that all computable functions of one variable can be obtained in this fashion.
1.845 seconds.