* Two compact Hausdorff spaces X < sub > 1 </ sub > and X < sub > 2 </ sub > are homeomorphic if and only if their rings of continuous real-valued functions C ( X < sub > 1 </ sub >) and C ( X < sub > 2 </ sub >) are isomorphic.

Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same.

Tower One is fully occupied by Petronas and a number of its subsidiaries and associate companies, while the office spaces in Tower Two are mostly available for lease to other companies.

Two parallel strips of stores faced the parking lot with a courtyard that had green spaces, benches, and entrances to the stores.

Two fluid-filled outer spaces ( scalae ) are formed by this dividing membrane.

Two spaces X and Y are homotopy equivalent if they can be transformed into one another by bending, shrinking and expanding operations.

Two morphisms can be composed to form a new morphism, and we obtain the category of ringed spaces and the category of locally ringed spaces.

Two n-dimensional quadratic spaces ( V, Q ) and ( V ′, Q ′) are isometric if there exists an invertible linear transformation ( isometry ) such that

Two metric spaces X and Y are called isometric if there is a bijective isometry from X to Y.

Two representations of G on vector spaces V, W are equivalent if they have the

Two vector spaces over the same field with the same dimensionality are always isomorphic ; but not necessarily in a natural or canonical way.

Two levels of luxury suites occupy spaces behind sliding glass doors above and below the club tier.

Two submanifolds M and N intersect transversally if at each point of intersection p their tangent spaces and generate the whole tangent space at p of the total manifold.

Two “ headless ” applications are also running in their own spaces, providing file and web services.

The Two main campuses ( Stoke-on-Trent and Stafford ) and the Lichfield campus all have purpose built Business Villages ; which consist of fully furnished small office spaces with full internet access included.

UNO is in the process of revising its Master Plan to include additional, state-of-the art student housing, a new University Center, Phase Two of the Research and Technology Park, new landscaping and student-centered outdoor learning spaces.

Two adjacent spaces are insufficient to make two eyes as well, since putting a stone in will create one eye only.

Two diagnostic symptoms of decline — or as many historians prefer, ' transformation '— are subdivision, particularly of expansive formal spaces in both the domus and the public basilica, and encroachment, in which artisanal shops invade the public thoroughfare, a transformation that was to result in the souk.

Two out of every five bars or spaces are wide ( hence exactly 2 of 5 ).

Two more wild card spaces were added to the board and the prize for matching them was reduced to $ 250.

Two albums-" Modern Pipe Organ " and " Autumn Nocturne " were recorded for Warner Brothers, as well as two albums done in conjunction with arranger Monty Kelly, one of which contained an arrangement of Richard Rodgers ' Slaughter on Tenth Avenue, and the other of which contained transcriptions of big band arrangements with spaces for the organ.

* Two exhibition spaces are dedicated to showing his work: the Oscar Howe Art Gallery at the Dakota Discovery Museum in Mitchell, and the Oscar Howe Gallery at the University of South Dakota in Vermillion, South Dakota.

* Two intimate 80-120 seat spaces with flexible seating arrangement ( Parade Studio and Space )

The American philosopher W. V. O. Quine, in his " Two Dogmas of Empiricism ", famously challenged the distinction, arguing that the two have a blurry boundary.

Two lords – Theobald V, Count of Blois, son of the Count of Champagne, and Geoffrey, Count of Nantes ( brother of Henry II, Duke of Normandy ) – tried to kidnap Eleanor to marry her and claim her lands on Eleanor's way to Poitiers.

Two Cities Films, an independent production company also made some important films including This Happy Breed ( 1944 ), Blithe Spirit ( 1945 ) and Sir Laurence Olivier's Henry V ( 1944 ) and Hamlet ( 1948 ).

He was very active in furthering the accession of the French candidate for the throne of Spain, Philip V. Two years later, Vendôme having died in the interval, Alberoni was appointed consular agent for Parma at Philip's court, where he was the royal favourite, being raised at the same time to the dignity of count.

Two years later, faced with a united Moroccan demand for the sultan's return, rising violence in Morocco, and the deteriorating situation in Algeria, the French government brought Mohammed V back to Morocco.

Two scholars, V. J. Rosivach and N. E. Andrews, have made interesting observations about stagecraft in Plautus: V. J. Rosivach writes about identifying the side of the stage with both social status and geography.

The war was fought primarily by forces supporting the unification – the Spanish loyal to Philip V, France, and the Electorate of Bavaria, together known as the Two Crowns – against those opposing unification – the so-called Grand Alliance among the Spanish loyal to Archduke Charles, the Holy Roman Empire, Great Britain, the Dutch Republic, Portugal and the Duchy of Savoy.

Two important anti-phagocytic antigens, named F1 ( Fraction 1 ) and V or LcrV, are both important for virulence.

Two similar concepts in contemporary English law are natural justice ( which generally applies only to decisions of administrative agencies and some types of private bodies like trade unions ) and the British constitutional concept of the rule of law as articulated by A. V. Dicey and others.

Two major losses that led to the end of the kingdom were in 197 BC when Rome defeated Philip V, and 168 BC when Rome defeated Perseus.

At the same time Andrzej Wajda began his work as a director in theatre, including such as Michael V. Gazzo's A Hatful of Rain ( 1959 ), Hamlet ( 1960 ), and Two for the Seesaw ( 1963 ) by William Gibson.

The I – V curve s of four devices: Two resistor s, a diode, and a Battery ( electricity ) | battery.

Two disjoint closed subsets A and B of a topological space X are said to be separated by neighbourhoods if there are neighbourhoods U of A and V of B that are also disjoint.

Two serogroups of V. cholerae, O1 and O139, cause outbreaks of cholera.

Two years later, Charles V signed the New Laws ( which replaced the Laws of Burgos of 1512 ) prohibiting slavery and the repartimientos, but also claiming as his own all the American lands and all of the autochthonous people as his own subjects.

There are four Canadian citizens within the Canadian Royal Family: Two married into it: In 1988, Sylvana Jones ( née Tomaselli in Placentia, Newfoundland ) wed the Earl of St. Andrews, a great-grandson of King George V, and, on 18 May 2008, Autumn Kelly, originally from Montreal, married Queen Elizabeth II's eldest grandson, Peter Phillips.

Thereafter it shared the fate of the Kingdom of Naples — including the period of Spanish rule of which the 16th-century castle of Charles V, overlooking modern Crotone, serves as a reminder — and its successor, the Kingdom of the Two Sicilies, which was conquered by the Kingdom of Sardinia in 1860 and incorporated into the new Kingdom of Italy in 1861.

Two years later, Antiochus V was greatly weakened because Rome sent an emissary to sink his ships and hamstring his elephants for his violation of the Peace of Apamea, storing up too much weaponry.

* Two vectors, x and y, in an inner product space, V, are orthogonal if their inner product is zero.

* Two vector subspaces, A and B, of an inner product space, V, are called orthogonal subspaces if each vector in A is orthogonal to each vector in B.

Two vertical diabase dikes, made up of highly impermeable igneous basalt parent rock, cut through the limestone bedrock in the area and form a subterranean " V ", with Boiling Springs located at the interior tip of the V.

Two of the other pins were used for + 5 V power supply and ground.