Instead, with the topology of compact convergence, C ( a, b ) can be given the structure of a Fréchet space: a locally convex topological vector space whose topology can be induced by a complete translation-invariant metric.

Instead, the Ottoman Navy spent the first two months of the war in operations against the Bulgarians in the Black Sea, giving the Greeks valuable time to complete their preparations and allowing them to consolidate their control of the Aegean.

Instead of seeking to administer the empire through counts, as Charlemagne had done and as his successors had attempted, Henry allowed the dukes of Franconia, Swabia and Bavaria to maintain complete internal control of their holdings.

Instead of constantly having to decode instructions and then fetch the data needed to complete them, it reads a single instruction from memory, and " knows " that the next address will be one larger than the last.

Instead he devoted more than a month to the preparation of a complete history of the electoral counts over the previous century to show it was the unbroken usage of Congress, not of the President of the Senate, to count the electoral votes.

Instead of pushing forward and creating a distinctive style, it treads over familiar gangsta territory, complete with bottomless bass, whining synthesizers, and meaningless boasts.

" Instead of implementing Barry's proposals, the newly Republican Congress ( who had come to power on promises of decreasing federal spending ) placed several city operations into receivership and created the District of Columbia Financial Control Board to assume complete authority over the city's day-to-day spending and finances, including overrule of the mayor's fiscal decisions.

:; Turnout: Instead of a complete spiral volute, a turnout is a quarter-turn rounded end to the handrail.

Instead, the Ottoman Navy spent the first two months of the war in operations against the Bulgarians in the Black Sea, giving the Greeks valuable time to complete their preparations and allowing them to consolidate their control of the Aegean.

Instead of supplying complete combat divisions, its function was to round out regular formations by supplying units of up to battalion size ( including infantry, light artillery and formation reconnaissance ), and to supply extra support functions such as engineers, medical units and military police.

Instead, for example, a rectangular outline of the window might be drawn during the drag, with the complete window contents being redrawn only once the user had released the mouse button.

It turns out that in a complete market with no arbitrage opportunities there is an alternative way to do this calculation: Instead of first taking the expectation and then adjusting for an investor's risk preference, one can adjust, once and for all, the probabilities of future outcomes such that they incorporate all investors ' risk premia, and then take the expectation under this new probability distribution, the risk-neutral measure.

Instead, he appointed the Sri Guru Granth Sahib, the Sikh holy book, as his successor as Guru instead of a possibly fallible human ; and due to the faith's belief in complete equality, women can participate in any religious function and / or perform any Sikh ceremony and / or lead the congregation in prayer.

Instead, she devoted her time to two projects: preserving Tanguy ’ s reputation through retrospective shows and a complete catalogue of his work, and writing poetry, mostly in the slangy French she had learned in her youth and spoken with Tanguy.

Instead of cliques, if the same question is asked for complete multi-partite graphs, the answer is given by the Erdős – Stone theorem.

Instead of coming to a complete stop, the rider makes a continuous " S " path by leaning left and right.

Instead, the QR algorithm works with a complete basis of vectors, using QR decomposition to renormalize ( and orthogonalize ).

Instead, Begin spoke of the historic unity of Israel in the West Bank, even hinting that he would make territorial concessions in the Sinai as part of a complete peace settlement.

Instead, a bridge had to be fashioned in situ — a task that would take until 3 April to complete.

Instead, by the time it debuted, Advanced Squad Leader had become a complete replacement of the games of the original SL series.

Instead, Radical wanted to steer the franchise's video game series in a different direction by giving the game engine a complete overhaul.

Instead, his loose association with George Panu signified a return to radicalism, and saw him campaigning in favor of universal suffrage and a complete land reform — this clashed with the views he had expressed earlier in life, and Caragiale was careful not to let it seem that he had returned to the " Red " liberalism of his youth.

Instead of rotating one position, any number relatively prime to will generate a complete schedule.

Instead of management having to coerce labor to work harder, labor volunteers to complete the project on-time.

Instead of emotional recrimination, loaded phrases and sloganeering, we need a dispassionate study of the facts, a better understanding of the opposite viewpoint and a more serious effort to extend the areas of agreement until a solution is reached.

Instead of enabling the guest operating system to dialog with hardware, virtual device drivers take the opposite role and emulate a piece of hardware, so that the guest operating system and its drivers running inside a virtual machine can have the illusion of accessing real hardware.

Instead, counterbalanced, wheeled ploughs, known as balance ploughs, were drawn by cables across the fields by pairs of ploughing engines which worked along opposite field edges.

Instead, growers reproduce the plant by cutting: they remove sections of the vine with six or more leaf nodes, a root opposite each leaf.

# Viruddha: Instead of proving something it is proving the opposite.

Instead of denial of services to low-income neighborhoods, sometimes the exact opposite can occur as well when it is the most lucrative option for the service providers.

Instead of considering AR and VR as exact opposite concepts, Milgram et al.

Instead, the magnet sample chamber has windows on two opposite sides.

Instead, she was assigned opposite teen idol Mickey Rooney in the Andy Hardy film Love Finds Andy Hardy ( 1938 ).

Instead the rebels bypassed Wade's army at Newcastle, by heading down the opposite coast via Carlisle.

Instead, of ILECs encroaching on each other, the opposite occurred-mergers.

Instead, a segmented shell gland forms on one side of the larva, and a foot forms on the opposite side.

Instead of each cylinder having a single piston and being closed at one end with a cylinder head, the Jumo-based design used an elongated cylinder containing two pistons moving in opposite directions towards the centre.

Instead she free-lanced at Warner Bros. with Mario Lanza and Joan Fontaine in Serenade ( 1956 ), directed by Anthony Mann, and at RKO in Samuel Fuller's Run of the Arrow ( 1957 ), opposite Rod Steiger and Charles Bronson.

Instead the church has formally stated that, due to matters of spirituality, the United Order and communism are materially opposite in purpose:

Instead of agricultural technology and scale determining and limiting population as Malthus attempted to argue, Boserup argued the world is full of cases of the direct opposite: that population changes and expands agricultural methods.

Instead of feeding both the bias signal and the audio signal into the same recording head, a few brands of audio tape recorder, notably Tandberg, Akai and its US cousin Roberts, used a separate bias head on the opposite side of the tape from the recording head ; this system was termed cross-field.

Instead, ventilation overshoots and can generate an opposite disturbance to the original disturbance.

Instead the opposite is true.

Instead, the wolfers arrived in the Battle Creek valley where the trading posts operated by Abel Farwell and Moses Solomon were located, opposite a camp of some 200 to 300 Nakota people.

Instead, one has to find an area with very low ground conductivity ( a requirement opposite to usual radio transmitter sites ), bury two huge electrodes in the ground at different sites, and then feed lines to them from a station in the middle, in the form of wires on poles.

Instead of assuming that democratization will provide a political outlet for resolving conflicts of competing values and interests and thus for putting an end to major forms of destabilizing violence, Etzioni argues, a Security First foreign policy is centered on precisely the opposite assumption: democratization requires security first.

Instead of an open track with covered cars, this ride was designed the opposite from the Disneyland version: open-air cars with a ceiling over the track.

" Instead of increasing new store openings each year as McDonald's financial base expanded, Sonneborn did the exact opposite .(..