Conversely, there are Grothendieck topologies which do not come from topological spaces.

Any point x gives rise to a continuous function p < sub > x </ sub > from the one element topological space 1 ( all subsets of which are open ) to the space X by defining p < sub > x </ sub >( 1 ) = x. Conversely, any function from 1 to X clearly determines one point: the element that it " points " to.

Conversely, given any topological space X, the collection of subsets of X that are clopen ( both closed and open ) is a Boolean algebra.

Conversely, any locale A has a topological space S ( A ) that best approximates the locale, called its spectrum.

Conversely, a current of one ampere is one coulomb of charge going past a given point per second:

Conversely, underclocking trades off slower operation to reduce power consumption and temperature, cooling requirements ( and therefore the number and speed of fans, allowing quiet operation ) and, where relevant, increase battery life per charge.

Conversely, at the cathode the copper ( II ) cations accumulate to maintain this neutral charge.

Conversely, a subset R defines a binary function if and only if, for any x in X and y in Y, there exists a unique z in Z such that ( x, y, z ) belongs to R.

Conversely, if ƒ: C → C is a function which is differentiable when regarded as a function on R < sup > 2 </ sup >, then ƒ is complex differentiable if and only if the Cauchy – Riemann equations hold.

Conversely, if the amount of fat is increased, increasing the number of calories ingested will only add weight.

Conversely every partition of comes from an equivalence relation in this way, according to which if and only if and belong to the same set of the partition.

Conversely, in functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function f twice with the same value for an argument x will produce the same result f ( x ) both times.

Conversely, if the data are sparse — that is, if only K out of N Fourier coefficients are nonzero — then the complexity can be reduced to O ( K log N log ( N / K )), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for N / K > 32 in a large-N example ( N = 2 < sup > 22 </ sup >) using a probabilistic approximate algorithm ( which estimates the largest K coefficients to several decimal places ).

Conversely, the symbol width could be set at 8, even if only values 0 and 1 are used ; these data would only require a 2-color table.

Conversely we have a b if and only if a < b or a ~ b. This is the reason for using the notation ""; "≤" can be confusing for a preorder that is not anti-symmetric, it may suggest that a ≤ b implies that a < b or a

Conversely, Baptists are underrepresented, a reflection of their quite recent expansion in numbers ; there has been only one Roman Catholic president, although they are currently the largest single denomination, and there have been no Lutheran, Pentecostal, or Latter Day Saint presidents.

Conversely, birds of prey-which show distinct reverse sexual dimorphism — tend to be monogamous for long periods or mate for life ; some species like the Snail kite will choose new mates every year, polygyny is noted in many Harriers and polyandry has been observed in the Harris ' Hawk ( notable for being the only bird of prey to regularly live and hunt in family and social groups ) and the aforementioned Galapagos hawk.

Conversely, a metrizable space is separable if and only if it is second countable, which is the case if and only if it is Lindelöf.

Conversely, only the wiki users interested in a given project need look at its associated wiki pages, in contrast to high-traffic mailing lists which may burden subscribers with many messages, regardless of their relevance.

Conversely, jumper classes are scored objectively, based entirely on a numerical score determined only by whether the horse attempts the obstacle, clears it, and finishes the course in the allotted time.

Conversely, if children are found to only develope after undergoing treatment it would challenge the traumagenic model.

Conversely, of the 253 known stable nuclides, only five have both an odd number of protons and odd number of neutrons: hydrogen-2 ( deuterium ), lithium-6, boron-10, nitrogen-14, and tantalum-180m.

Conversely, a German controlled major rail head lay only to the north of their positions.

Conversely, a wing dam is a structure that only partly restricts a waterway, creating a faster channel that resists the accumulation of sediment.

Conversely, a small farm surrounding the owner's dwelling is called a smallholding and is generally focused on self-sufficiency with only the surplus being sold.

Conversely, abstract patterns in science, maths, or language may be observable only by analysis.

Conversely, Hill would play only 47 games in the following four seasons due to a recurring ankle injury.

Conversely, even though nearly 60 percent of voters selected the Democratic Governor Gary Locke in 2000, in 2004 the Democratic gubernatorial nominee Christine Gregoire received only 41 percent of the vote.

Conversely, North Korea refused to speak in the context of six-party talks, stating that it would only accept bilateral talks with the United States.

Conversely, following the diurnal motion with the camera, to eliminate it on the photograph, can best be done with an equatorial mount, which requires adjusting the right ascension only ; a telescope may have a motor to do that automatically ( sidereal drive ).

Conversely, most modern role-playing games encourage gamemasters to ignore their gaming systems if it makes for a more enjoyable story, even though they may not describe themselves as " storytelling " games.

Conversely, the exemplary stepmother prefers the stepson to her own child, in recognition that his seniority makes him superior.

Conversely the Royal Navy, which includes the Royal Marines, makes no distinction between postings at sea or on land.

Conversely, the strong interaction between electrons and proteins makes thick ( e. g. 3-dimensional > 1 micrometer ) crystals impervious to electrons, which only penetrate short distances.

Conversely, in times of robust economic growth, fixed investment will increase across the board, because the observed market expansion makes it likely that such investment will be profitable in the future.

Conversely, British English favours fitted as the past tense of fit generally, whereas the preference of American English is more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i. e., suited ) for a purpose ; in spatial transitive contexts, AmEng uses fitted for the sense of having made an object conform to an unchanged object that it surrounds ( e. g., " fitted X around Y ") but fit for the sense of having made an object conform to an unchanged object that surrounds it ( e. g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive ) of having been matching with respect to contour, with no alteration of either object implied, AmEng prefers fit (" The clothes fit.

Conversely, most realists ( specifically, indirect realists ) hold that perceptions or sense data are caused by mind-independent objects.

Conversely, given a groupoid G in the algebraic sense, let G < sub > 0 </ sub > be the set of all elements of the form x * x < sup >− 1 </ sup > with x varying through G and define G ( x * x < sup >-1 </ sup >, y * y < sup >-1 </ sup >) as the set of all elements f such that y * y < sup >-1 </ sup > * f * x * x < sup >-1 </ sup > exists.

Conversely, the rejection of syncretism, usually in the name of " piety " and " orthodoxy ", may help to generate, bolster or authenticate a sense of uncompromised cultural unity in a well-defined minority or majority.

Conversely, in the category of rings, there are no kernels in the category-theoretic sense ; indeed, this category does not even have zero morphisms.

" Conversely, in the positive sense, it would refer to " having it both ways " or " having the best of both worlds.

Conversely, any operator satisfying the above properties defines a connection on E and a connection in this sense is also known as a covariant derivative on E.

Conversely, those who had a difficult time during middle adulthood may look back and feel a sense of despair.

Conversely, an Ehresmann connection H ⊂ TP ( or v: TP → V ) on P defines a principal G-connection ω if and only if it is G-equivariant in the sense that.

Conversely, synthetic languages often combine many lexical morphemes into single words, making it difficult to boil them down to the traditional sense of words found more easily in analytic languages ; this is especially difficult for polysynthetic languages, such as Inuktitut and Ubykh, where entire sentences may consist of a single word.

for all compactly supported functions ƒ and h. Conversely, () characterizes Δ completely, in the sense that it is the only operator with this property.

Conversely and to some surprisingly, the word may be used to mean " approve of ," especially in an official sense.