Although officially declassified, the original film taken by U. S. Corona spy satellite in the 1960s has been altered prior to declassification ; in answer to freedom of information queries, the government responds that these exposures ( which map to Groom and the entire NAFR ) appear to have been destroyed .< ref >

Using the above theorem it is easy to see that the original Borsuk Ulam statement is correct since if we take a map f: S < sup > n </ sup > → ℝ < sup > n </ sup > that does not equalize on any antipodes then we can construct a map g: S < sup > n </ sup > → S < sup > n-1 </ sup > by the formula

A map showing the original boundaries of Cambridge

When Chicago was founded in 1833, most of the early building began around the mouth of the Chicago River, as can be seen on a map of the city's original 58 blocks.

This smaller map has the condition that if it can be colored with four colors, then the original map can also.

This implies that if the original map can not be colored with four colors the smaller map can't either and so the original map is not minimal.

The original Gamma World boxed set ( containing a 56-page rulebook, a map of a devastated North America, and dice ) was released in 1978.

Compression is successful if the resulting sequence is shorter than the original sequence plus the map needed to decompress it.

Since the creation of the original LambdaMOO map, many users have expanded the MOO by making additional rooms with the command "@ dig.

A 1902 lithograph map ( original size 33 × 24 cm )

This syntax uses a string of ASCII characters indicating both the original character encoding ( the " charset ") and the content-transfer-encoding used to map the bytes of the charset into ASCII characters.

The original city map of New Amsterdam called Castello Plan from 1660 ( the bottom left corner is approximately south, while the top right corner is approximately north )

On October 11, 2006, John Romero released the original map files for all of the levels in Quake under the GPL.

The original rules contained a map of an area called Dragon Pass, a region offered as the default setting for adventures.

The massive mountain does not appear on a map of the original Ringworld, leading Louis to conclude that it is in fact the result of a meteor impact with the underside of the ring, which pushed the " mountain " up from the ring floor and broke through.

Today, the Tube map bears the legend, " This diagram is an evolution of the original design conceived in 1931 by Harry Beck " in the lower right-hand corner.

Nevertheless the map remains true to Beck's original scheme, and many other transport systems use schematic maps to represent their services, likely inspired by Beck.

Despite there having been many versions over the years, somehow the perception of many users is that the current map actually is, more or less, Beck's original version from the 1930s — a testament to the effectiveness of his design.

Although he did not attend any celebrated schools or universities, he was a master of Greek and Hebrew and could read the Bible in the original.

For by now the original cause of the quarrel, Philip's seizure of Gascony, was only one strand in the spider web of French interests that overlay all western Europe and that had been so well and closely spun that the lightest movement could set it trembling from one end to the other.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

Laudably enough, it is offering classics and off-beat imports, but last week only one U.S. original was on the boards, Robert D. Hock's stunning Civil War work, Borak.

Stowey Rummel was internationally famous, a crafter of a genuine Americana in foreign eyes, an original designer whose inventive childishness with steel and concrete was made even more believably sincere by his personality.

He claims that he was denied due process of law in violation of the Fifth Amendment, because ( 1 ) at a hearing before a hearing officer of the Department of Justice, he was not permitted to rebut statements attributed to him by the local board, and ( 2 ) at the trial, he was denied the right to have the hearing officer's report and the original report of the Federal Bureau of Investigation as to his claim.

Petitioner was not entitled, either in the administrative hearing at the Department of Justice or at his trial, to inspect the original report of the Federal Bureau of Investigation, since he was furnished a resume of it, did not challenge its accuracy, and showed no particular need for the original report.

He says that he was not permitted to rebut before the hearing officer statements attributed to him by the local board, and, further, that he was denied at trial the right to have the Department of Justice hearing officer's report and the original report of the Federal Bureau of Investigation as to his claim -- all in violation of the Fifth Amendment.

That Prokofieff's harmonies and forms sometimes seem professionally routine to our ears, may or may not indicate that he was less of an `` original '' than we prefer to believe.

This original capsule contained a battery and a transistor oscillator and was about 1 cm. in diameter.

when the insoluble fraction was suspended in a volume of saline equal to that of the original serum sample, no complete antibody activity could be detected.

Approximately ten days after the questionnaire was mailed, a follow-up airmail postcard was sent to each of the original names.

In parts a repeated sponging was needed, but everywhere we found that water alone was enough to restore the original brightness.

Down in Concord, New Hampshire, was a flier in the right place at the right time: Robert S. Fogg, a native New Englander, had been a World War 1, flying instructor, barnstormer, and one of the original planners of the Concord Airport.

`` To be creative is to have the ability to cause to exist -- to produce where nothing was before -- to bring forth an original production of human intelligence or power ''.

What remained lacked the original verve but it was at least dignified, as befitting the tragic circumstances.

In the late 1980s Moog repaired the original theremin of Clara Rockmore, an accomplishment he considered a high point of his professional career.

While the original rail has long since been replaced because of age and wear, and the roadbed upgraded and repaired, the lines generally run on top of the original, handmade grade.

This therefore " bricks " the device, rendering it unusable for its original purpose until it can be repaired or replaced.

In accordance with this determination the leaden mortuary chest containing the remains of Harvey was repaired, and was, as far as possible, restored to its original state ... "

A repaired spiral staircase leads up to the top of the southeast corner tower, affording views of the surrounding town and countryside, including the original castle motte to the southwest.

The original 20x30 foot screen was salvaged, but needed to be repaired.

The original crane sculpture, which was at the top of the fountain, was lost in storage until 2005, when it was cleaned, repaired and replaced on the fountain.

Vegetation was cleared, stonework repaired, and the original floor level re-established throughout the castle.

The airport's original control tower, built in the 1950s, is now located in the airport's passenger terminal and used as a ground control tower, after being repaired from damages caused by the Nisqually Earthquake in 2001.

Over the summer of 2007, the main facade of Rideau Hall underwent a major renovation by the National Capital Commission, that saw the masonry treated and restored, the original sash windows rehabilitated and stripped of their lead paint, and the copper roof of the Mappin Wing repaired.

Because the summit cross could no longer be repaired, a replica was made that was true to the original cross.

Unfortunately after the war the damage was never repaired and the pier never regained its original length.

From 17 December 2008 the scaffolding for the repaired roof has been removed and the platform restored to its original state.

By the middle part of the 18th century it had fallen into disrepair and was repaired and refurbished around 1777 retaining the original medieval tower.

Changes made before the final version were filmed include a thunderclap sound effect being deleted from the opening theme music ; Susan's dress being changed to make her look more like a schoolgirl than the original costume, which made her appear more alien and sensual ; the Doctor's costume being changed from a contemporary jacket and tie to his familiar Edwardian clothing ; a reference to the Doctor and Susan being from the 49th century was replaced with the line " another time, another world "; the TARDIS door being repaired so that it closed properly ; and a refinement of the TARDIS sound effect.

As was usual, the walls were left breached after this siege but the Berkeley family were allowed to retain ownership on condition that they never repaired the damage to the Keep and Outer Bailey, still enforced today by the original Act of Parliament drawn up at the time ; according to Pevsner, the breach is partially filled by a subsequent ' modern ' rebuild, but this only amounts to a low garden wall, to stop people falling 28 ' from the Keep Garden, the original Castle's " motte ".

Professor Angelo Bottini, Superintendent of Archeology in Rome, stated that an awning or tent covering is in place to protect the ancient relics until the covering is repaired, giving tourists of this millennium a look at the original suggestum for the first time in 50 years.

It has been repaired so often that none of the original broom remains, having had both the shaft and bristles repeatedly replaced and it often requires the user to pick up speed by running along the ground, making it the only broom on the Disc that requires bump starting.

The house subsequently changed hands several times in the ensuing period and steadily fell into a state of dilapidation until it ended up in the hands of Dr. Friedrich Schuster who had the building repaired again, getting rid of the 1846 modifications and reinstating its original Baroque appearance.

In the original Asimov books, it is unknown if Dors has been repaired after the damage.

The original painter from the 1996 opening was found to repaint the repaired sections.

Fryer re-finished the neck and body in the original Rustin's Plastic coating used in the creation over the existing finish, and fingerboard wear was repaired and dot-markers replaced.

Parking lots and paved roads were also removed, and the El Morro lighthouse repaired and restored to its original appearance.