Ultimately the Russian school of point-set topology, under the direction of Pavel Alexandrov and Pavel Urysohn, formulated Heine – Borel compactness in a way that could be applied to the modern notion of a topological space.

Ultimately these plans failed because he could not reach a consensus with the powerful Islamist factions.

Ultimately, the system as it stood could not deal quickly enough with the large deficits and surpluses created in the balance of payments ; this has previously been attributed to increasing rigidity of wages ( particularly in terms of wage cuts ) brought about by the advent of unionized labor, but is now more likely thought of as an inherent fault with the system which came to light under the pressures of war and rapid technological change.

Ultimately, his unbending austerity could not inspire the devotion needed to hold his conquests together.

Ultimately, the parlement de Paris agreed that " all traditional observances should be carefully maintained to avoid the impression that the Estates-General could make things up as it went along.

Ultimately it made for a very flexible system with a vast array of options, but could easily suffer from play balance problems if particular sets of rules were used together, since little effort was made to balance different variants against each other, and power creep in the later professions and spell lists was very much in evidence.

Ultimately, however, his primary passion was still practical optics, once noting that " In all my experiments I could, owing to lack of time, pay attention to only those matter which appeared to have a bearing upon practical optics ".

" His review concludes " Ultimately, the one force the rebels could not overcome proved to be the BBC's long-standing apathy towards science fiction.

Ultimately, the league could not survive the arrival of affiliated baseball to Montgomery.

Ultimately, Uruk could not maintain long-distance control over colonies such as Tell Brak by military force.

Ultimately, if there was no veto, and the matter was of minor importance, it could be voted on by a voice vote or by a show of hands.

Ultimately, the British Foreign Office decided that Kolchak could do more for the Allied cause by toppling Vladimir Lenin and the Bolsheviks and bringing Russia back into the war on the Allied side.

Ultimately, the Army's Generals ( particularly Oliver Cromwell ) could rely both on the Army's internal discipline and its religious zeal and innate support for the " Good Old Cause " to maintain an essentially dictatorial rule.

Ultimately, Bartlett argued that the mistakes that the participants made could be attributed to schematic intrusions.

Ultimately, it was believed, enough individual unions could be won over that the entire trade union movement could be moved in a socialist direction.

Ultimately, the Red Dragon conspirators could not obtain the necessary financial backing for their plans and dissolved the conspiracy after a failed revolutionary attempt by Sun Yat-sen ’ s followers in March 1911.

Ultimately he chose Fox, believing he could control him easier than Pitt.

Ultimately, the target was not met and only a single track between Loughborough and Quorn could be afforded ( BR allowed more time to raise funds to purchase Quorn to Rothley ).

Ultimately the backup service must itself use one of the above methods so this could be seen as a more complex way of doing traditional backups.

Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic.

Ultimately, economic stagnation in the Soviet Union could only have been caused by internal problems rather than external.

Ultimately, the constrained vision demands checks and balances and refuses to accept that any one person could put aside their innate self-interest.

Ultimately, O ' Malley and Moses could never come to agreement on a new location for the Dodgers, and the club moved west to Los Angeles.

Ultimately, Hall failed to forge a lasting alliance with the New Left.

Ultimately, a compromise was negotiated, bringing the countess a substantial fortune, from which she paid Lassalle an annual income of 5000 thalers ( about £ 750 ) for the rest of his life.

Ultimately, in 1768, both agreed to not run for office, and Josias Lyndon was elected governor of the colony as a compromise candidate.

Ultimately if backbenchers are unhappy with the leadership's position they can threaten to revolt during a vote and force the leadership to compromise.

Ultimately, a compromise was reached, and while the Consulship remained closed to the Plebeians, Consular command authority ( imperium ) was granted to a select number of Military Tribunes.

Ultimately, Crittenden's position prevailed, and a compromise with Britain was effected, setting the dividing line between the two nations ' claims at the 49th parallel north.

Ultimately, the Rhodians reached a compromise with Demetrius – they would support Antigonus and Demetrius against all enemies, save their ally Ptolemy.

Ultimately though, a compromise was reached and thereafter, the phrase ' Tiswas presents The Four Bucketeers ' was used.

Ultimately, a compromise is reached that will result in the pair ‘ sharing ’ Mr. Sloane a few months at a time.

Ultimately the committee negotiated a compromise.

Ultimately, he was forced to compromise and introduced an amendment removing the references to treason.

Ultimately, portions of Smoot's amendments were combined with those of other Senators to create a compromise.

Ultimately, the King had to compromise and divorced her formally, refusing, however, to marry anyone else.

Ultimately market forces and real needs determine the selection of problem solutions and related technologies, also among those proposed by research.

Ultimately, there is no way to measure whether a particular phylogenetic hypothesis is accurate or not, unless the true relationships among the taxa being examined are already known ( which may happen with bacteria or viruses under laboratory conditions ).

Ultimately, Satan is thrown into the " Lake of fire ", not as ruler, but as one among many, being tormented day and night forever and ever.

Ultimately, the system was referred to as the Synclavier Digital Recording " Tapeless Studio " system among many professionals.

Ultimately, the delegates elected to call the new country the Dominion of Canada, after " kingdom " and " confederation ", among other options, were rejected for various reasons.

Ultimately, in 1258, the King was forced to accept the Provisions of Oxford, which prohibited, among other things, the creation of new forms of writ without the sanction of the King's council.

Ultimately, none of these motives is identified as primary, so it is impossible to determine conclusively which applies, if indeed any of them do in isolation, or which is most important among them.

Ultimately, the act's technical failures were exploited by both the union officials – most famously the Teamsters, whose president, Jimmy Hoffa, among others, notably raided the union pension coffers for his own personal investments – and the courts.

Ultimately, the employer, not the Department of Labor, determines what source it will use to determine the prevailing wage for an offered position, and it may choose among a variety of competing surveys, including its own wage surveys, provided that such surveys follow certain defined rules and regulations.

Historian Paul Walker writes: “ Ultimately, both views of him, the mad and despotic tyrant irrationally given to killing those around him on a whim, and the ideal supreme ruler, divinely ordained and chosen, whose every action was just and righteous, were to persist, the one among his enemies and those who rebelled against him, and the other in the hearts of true believers, who, while perhaps perplexed by events, nonetheless remained avidly loyal to him to the end.

Ultimately nothing has come of them, the likely negative impact on prices for any downgraded châteaux and the 1855 establishment's political muscle are considered among the reasons.

Ultimately, this proved unsuccessful, and NYU decided not to negotiate a second contract with the Graduate Student Organizing Committee, sparking a strike among graduate assistants in late 2005 and criticism of Sexton.

Ultimately, whether the firm constitutes a domain of bureaucratic direction that is shielded from market forces or simply “ a legal fiction ”, “ a nexus for a set of contracting relationships among individuals ” ( as Jensen and Meckling put it ) is “ a function of the completeness of markets and the ability of market forces to penetrate intra-firm relationships ”.

Ultimately, this was agreed to and the United Kingdom enacted the Eire ( Confirmation of Agreements ) Act 1938, which put in effect, among other things, the British government's agreement to return the Treaty Ports.

Ultimately, inhumation would replace cremation ; a variety of factors, including the rise of Christianity among Romans and changes in attitudes to the afterlife, would contribute to this marked shift in popular burial practices.

Ultimately resolving issues among these viewpoints are matters for negotiation.

Ultimately, the Gene Tryp stage production was abandoned and among the twenty-six songs that McGuinn and Levy had written for the project, six ( including " Chestnut Mare ") would end up being released on The Byrds ' ( Untitled ) and Byrdmaniax albums.

Ultimately, the victorious Communists subsumed Tatarstan within the Russian Soviet Federative Socialist Republic ( RSFSR ), leading to large-scale emigration from the country, particularly among the upper class.

Ultimately, the ambivalence of labor groups led those within the Administration who supported NAFTA to believe that strengthening NAFTA ’ s labor side agreement too much would cost more votes among Republicans than it would garner among Democrats, and would make it harder for the United States to elicit support from Mexico.