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, Gorbachev could not forge a compromise among these forces and the consequence was the dissolution of the Soviet Union.

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, 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, the conflict between her devotion to the Church and the nursing profession, juxtaposed with her passionate Belgian patriotism and her love of her father ( killed by Nazi fighter planes while treating wounded ) bring her to an impasse, which serves as the dénouement of the novel.

Ultimately Prabhupada gives the conclusion that society should be " Krishna conscious " -- enlightened by devotion ( bhakti ) to Krishna ( God ).

Ultimately Washington decided that the Crips needed to be brought back under one umbrella organization ( as many new " sets " were formed after Washington and others went to jail ).

Ultimately he obtained this, and as Superior General he was then able to move brothers across diocesan boundaries to wherever they were most needed.

Ultimately, two such devices would be needed, their outputs to be combined as quadrature components of the complete solution.

Ultimately unsuccessful in preventing the 1745 uprising and not needed after the Highland Clearances, the Bernera Barracks are now ruined.

Ultimately, the interview proved to be enough evidence needed ( since there weren't any known witnesses to the assault ) to earn Shakur a 15 day jail sentence.

Ultimately, Lil ' Slugger is a paranormal figment of Tsukiko's guilt and fear, brought inexplicably to life when the adult Tsukiko desperately needed to escape her responsibilities and then fed and nurtured by the fear of the populace.

Ultimately Netanyahu failed to hold the government together, and early elections for both Prime Minister and the Knesset were called in 1999.

Ultimately the town is intended to hold 5, 000 people.

Ultimately, the VVD opted for a coalition with the CDA, with VVD leader Mark Rutte as prime minister -- the first liberal to hold the post since 1918.

Ultimately the board was remembered for plans put on and off hold, and immense controversy.

Ultimately, it was the lack of a strong and unified religious orientation that enabled Islam to take hold in such high numbers in Bosnia, whereas other Turk dominions held onto their Catholic or Orthodox faiths.

" Ultimately the Supreme Court ruled that President George W. Bush does not have the sole authority to hold tribunals and is required to get authorization to do so from the United States Congress.

Ultimately he is asking if it would be expedient to hold elections now or better to put them off till spring.

Further, Ysbaddaden states that the only hound who can hunt Twrch is Drudwyn, the whelp of Greid, and then goes on to list the requirements of the leash to hold Drudwyn, the only man strong enough to hold the leash, & c. Ultimately Ysbaddaden calls on Culhwch to seek out Arthur, Culhwch's cousin, to help him hunt Twrch.

Ultimately, at the end of the campaign, Owain was forced to come to terms with Henry, being obliged to surrender Rhuddlan and other conquests in the east.

Ultimately, the Echolls family self-destructs when one of Aaron's sexual conquests, after seeing in the arms of yet another woman, stabs Aaron at a Christmas party, leading to the exposure of his chronic infidelity.