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, however, the Cubs wilted under pressure.

Ultimately, Britain and France both abandoned the concept of collective security in favour of appeasement in the face of growing German militarism under Hitler.

Ultimately, it failed to solve many of the problems with which it was centrally concerned, and after the Second World War, its doctrines increasingly came under attack by thinkers such as Nelson Goodman, Willard Van Orman Quine, J. L. Austin, Peter Strawson, Hilary Putnam, and Richard Rorty.

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, eleven territories were placed under trusteeship: seven in Africa and four in Oceania.

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Ultimately the emergency currency issued under the Aldrich-Vreeland Law was entirely withdrawn.

Ultimately, following the collapse of the German Democratic Republic on 3 October 1990, all planning projects under the socialist regime were abandoned.

Ultimately, Sauron advised him to attack Valinor and under the ruse that doing so would allow the king to claim immortality.

Ultimately, the city fell under Arab conquest in 643, by which time little was left of the opulent Roman cities of Northern Africa ; the ruins of Cyrene are located near the modern village of Shahhat.

Ultimately the film grossed a global total of $ 133, 000, 000, against its $ 21 million cost ($ 1 million under budget ).

Ultimately FitzGerald made his entry into party politics under the banner of Fine Gael.

Ultimately, it was a Hunanese army under Zeng Guofan who marched into Nanjing to put down the uprising in 1864.

Ultimately, Viacom purchased a minority share in the network, and rebranded it under the CMT name.

Ultimately the narrator's guilt manifests itself in the hallucination that the man's heart is still beating under the floorboards.

Ultimately, although I never intentionally put a banned substance into my body, the independent arbitrator ruled that I had to be suspended under the terms of the program.

Ultimately, command of Soviet efforts to relieve Stalingrad was put under the leadership of General Aleksandr Vasilevsky.

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, in 1904 the United States bought out the assets of the Company and resumed work under a revised plan.

Ultimately, the Christian Union under leadership of Spurling's son and others including a former Quaker and Bible salesman named Ambrose Jessup Tomlinson, experienced remarkable growth in the late 19th and early 20th centuries in the Appalachian foothills.

Ultimately, GSA made public amends by funding extensive scientific research under the auspices of Dr. Michael Blakey ; creating a new subagency, the Office of Public Education and Interpretation ; truncating the building plan ; and funding public reports on the story of the African Burial Ground.

Ultimately, the book ( released under Hornberger's pseudonym, Richard Hooker ), proved amazingly successful.

Ultimately the U. S. Congress is the only one who can make decisions regarding the political status of Puerto Rico, as stated under the Territorial Clause.

Ultimately the case turned on the credibility of his accuser, which was undermined when it was admitted she had lied consistently under oath throughout the trial.

Ultimately, pressure from other ITV companies ( notably Yorkshire Television ) forced Thames to sell them back to the distributor at a loss.

Ultimately, NSI was granted immunity from anti-trust litigation, but the litigation created enough pressure to restructure the domain name market.

Ultimately the U.N. army in the Congo reached a top strength of 19,000, including about 5,000 from India and a few soldiers from Eire and Sweden, who were the only whites.

Ultimately, the kingdom of Wessex occupied the southwest of England, but the initial stages in this expansion are not apparent from the sources.

Ultimately, those who persist in rejecting God condemn themselves, by cutting themselves off from the ultimate source of all Life, and from the God who is Love embodied.

Ultimately, the name change campaign lasted for a three year period from 1982 to 1984 ( Datsun badged vehicles had been progressively fitted with small " Nissan " and " Datsun by Nissan " badges from the late 1970s onward ) until the Nissan name was given prominence in 1983-although in some export markets vehicles continued to wear both the Datsun and Nissan badges until 1986.

Ultimately it was not clear that Jellicoe made any mistakes in his management of the fleet, nor departed from procedures which had been agreed upon by all concerned in advance.

Ultimately, Frederick prevailed in all those conflicts by outliving his opponents and sometimes inheriting their lands, as was the case with his nephew Ladislaus, from whom he gained Lower Austria in 1457, and with his brother Albert VI, whom he succeeded in Upper Austria.

Ultimately, key ferry links will be replaced with bridges, starting with one from Rosignol to New Amsterdam across the Berbice River.

Ultimately, Henry III was defeated and had to recognise Louis IX's overlordship, although the King of France did not seize Aquitaine from Henry III.

Ultimately, some, like John Shosky, have concluded " It is far from clear that any one person should be given the title of ' inventor ' of truth-tables.

Ultimately the name was taken from his own original kanji, 武蔵, which can be read as Takezō or as Musashi, as stated in Eiji Yoshikawa's book Musashi.

Ultimately the Lutici and the Obotrites were able to liberate themselves from the German rule for the next two centuries.

Ultimately the Soviet Army was withdrawn from Afghanistan in 1989 because of international opposition, persistent anti-Soviet guerilla warfare ( enhanced by the U. S .), and a lack of support from Soviet citizens.

Ultimately this resulted in the 1984 La Uribe Agreement, which called for a cease-fire, which ended up lasting from 1984 to 1987.

Ultimately, the original source for those languages is from the Tamil word அர ி ச ி ( arisi ).

Ultimately, the minister's strong support from Elizabeth, prevailed.

Ultimately, the word comes from Greek διαβαίνειν ( diabainein ), meaning “ to pass through ”, which is composed of δια-( dia -), meaning “ through ” and βαίνειν ( bainein ), meaning “ to go ”.

Ultimately, the United States ' proposals and actions did not stop the factors of European nationalism spawned by the previous war, the repercussions of Germany's defeat, and the failures of the Treaty of Versailles from plunging the globe into a Second World War.

Ultimately, it was a failure in personnel that spelt the end of the opposition against Edward I. Bohun died late in 1298, after returning from the Falkirk campaign.

Ultimately, many of them settled there permanently, in a land that became known as Normandy ( deriving from the expression " Nordmenn ", or ' Northmen ' (' Norsemen '), which was-and indeed still is-both the name the Norwegians called themselves and also the name the Franks used for the Scandinavians ).

Ultimately — like much fantasy — it draws from mythology and classical epics such as Homer's Odyssey and the Norse sagas.

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.