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Topic: Complete space


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  Complete space - Wikipedia, the free encyclopedia
In mathematical analysis, a metric space M is said to be complete (or Cauchy) if every Cauchy sequence of points in M has a limit that is also in M.
If this completion procedure is applied to a normed vector space, one obtains a Banach space containing the original space as a dense subspace, and if it is applied to an inner product space, one obtains a Hilbert space containing the original space as a dense subspace.
Completely metrizable spaces can be characterized as those spaces which can be written as an intersection of countably many open subsets of some complete metric space.
en.wikipedia.org /wiki/Complete_space   (1095 words)

  
 Completeness article - Completeness mathematics Metric spaces uniform spaces Cauchy sequence converges - What-Means.com   (Site not responding. Last check: 2007-10-20)
In category theory, a category C is called complete if every functor from a small category to C has a limit; it is called cocomplete if every such functor has a colimit.
Furthermore, an ordered field is complete if every non-empty subset of it that has an upper bound within the field has a least upper bound within the field, which should be compared to the (slightly different) order theoretical notion of bounded completeness.
In computational complexity theory, a problem P is said to be complete for a complexity class C, under a given type of reduction, if P is in C, and every problem in C reduces to P using that reduction.
www.what-means.com /encyclopedia/Complete   (646 words)

  
 Completeness - Wikipedia, the free encyclopedia
It should be noted that "complete" here is just a term that takes on specific meanings in specific situations, and not every situation in which a type of "completion" occurs is called a "completion".
In the particular case of Hilbert spaces (or more generally, inner product spaces), an orthonormal basis is a set that is both complete and orthonormal.
In computational complexity theory, a problem P is complete for a complexity class C, under a given type of reduction, if P is in C, and every problem in C reduces to P using that reduction.
en.wikipedia.org /wiki/Complete   (675 words)

  
 PlanetMath: complete measure
is said to be complete if every subset of a set of measure 0 is measurable (and consequently, has measure 0); i.e.
If a measure space is not complete, there exists a completion of it, which is a complete measure space
This is version 2 of complete measure, born on 2004-01-18, modified 2004-01-18.
planetmath.org /encyclopedia/Complete6.html   (83 words)

  
 Complete space : Completeness (topology)   (Site not responding. Last check: 2007-10-20)
In mathematical analysis, a metric space M is said to be complete if every Cauchy sequence of points in M has a limit in M. In mathematical analysis, a metric space M is said to be complete if every Cauchy sequence of points in M has a limit in M.
For instance, the rational numbers are not complete, because √2 is "missing".
Cantor's contsruction of the real numbers is a special case of this; the real numbers are the completion of the rational numbers using the ordinary absolute value to measure distances.
www.termsdefined.net /co/completeness-(topology).html   (1257 words)

  
 PlanetMath: complete
More generally, the completion of any metric space is a complete metric space.
-space of p-integrable functions is a complete metric space.
This is version 4 of complete, born on 2001-10-27, modified 2004-05-15.
planetmath.org /encyclopedia/Complete.html   (90 words)

  
 Complete space   (Site not responding. Last check: 2007-10-20)
In mathematical analysis, a metric space M is said to be complete if every Cauchy sequence of points in M has a limit in M.
By using different notions of distance on the rationals, one obtains different incomplete metric spaces whose completions are the p-adic numberss.
It is also possible to define the concept of completeness for uniform spaces using Cauchy netss instead of Cauchy sequences.
www.sciencedaily.com /encyclopedia/complete_space   (1119 words)

  
 Atlantis Crew Complete First Space Walk
Their most important task is to replace a charger and four of the six batteries needed to generate electricity for the ISS that no longer work.
Atlantis was launched Friday from the Kennedy Space Center on a delayed 10-day mission to repair the ISS and load equipment onto the station for use by crews arriving later this year.
The space station, assembled in December 1998, currently comprises two modules: the US-built Unity and the Russian module Zarya, with maintenance to the latter module the most pressing.
www.spacedaily.com /news/iss-00t.html   (623 words)

  
 BBC News | ISS | Astronauts complete marathon space walk
Two astronauts from the space shuttle, Discovery, have completed the first space walk as part of their work to equip the International Space Station for permanent residence.
The bulky space suits - known as extravehicular mobility units, or EMUs - were kept low on pressure during the EVA to make them more manoeuvrable.
Space walking is considered to be one of the most dangerous activities in the programme, after launches and landing.
news.bbc.co.uk /hi/english/special_report/iss/newsid_356000/356488.stm   (608 words)

  
 Amazon.co.uk: Video: Space - The Complete TV Series   (Site not responding. Last check: 2007-10-20)
Space is an ambitious six-part series from the BBC that follows their runaway successes Walking with Dinosaurs and The Planets into the realm of lavish computer animation.
Space shows us we spend too much time fighting amongst ourselves when there are far greater threats to all of us.
Space leaves the viewer to make up their own minds about the subjects covered and to want to find out more.
www.amazon.co.uk /exec/obidos/ASIN/B00005JHYQ   (1053 words)

  
 CNN.com - Cosmonauts complete space walk for repairs - December 3, 2001
It was a retrieval mission to get an errant rubberized o-ring seal that was hampering a hard dock between the Progress cargo ship and the international space station.
Space agency officials had correctly theorized that an obstruction was preventing hooks and latches from fully engaging to fasten the supply ship Progress to its docking port.
EST Tuesday, since it appears the space walkers succeeded on their makeshift repair job.
archives.cnn.com /2001/TECH/space/12/03/spacewalk   (331 words)

  
 SPACE.com -- Complete coverage of Mir   (Site not responding. Last check: 2007-10-20)
Alex Bowles was standing on a beach in Fiji as the Mir Space Station streaked to its final resting place in the South Pacific.
Yuri Semenov, president of RSC Energia, the aerospace company that manufactured and operated the space station Mir, officially confirmed Friday that Russia's ground tracking stations had not spotted the station overhead and it should now be presumed scuttled in the south Pacific.
Astrosociology is the study of astrosocial phenomena (social/cultural patterns related to space), a multidisciplinary field open to all scientists and engineers interested in "space and society" issues.
www.space.com /missionlaunches/missions/mir_fiery_finale_page.html   (522 words)

  
 BBC News | SCI/TECH | Grandads complete space mission
Ross is the American space agency's (Nasa) most experienced spacewalker with eight walks to his credit.
He is on a record seventh space flight.
Morin is a Navy doctor on his first space trip.
news.bbc.co.uk /hi/english/sci/tech/newsid_1929000/1929497.stm   (322 words)

  
 Medialunchbox - DVD : Lost in Space - The Complete First Season   (Site not responding. Last check: 2007-10-20)
I was 12 years old in the fall of 1965 when Lost in Space first came out, and I can still remember being riveted to my bw tv on Wednesday nights.
I was very well pleased with the "1st Season" of "Lost in Space", but I also wanted to be given the choice of seeing it in "Color" (Colorized), This is the only thing I felt disappointed about was not being given the choice between "Black and White" or "Color" (Colorized).
"Lost in Space" (1965-68) told the story of the space family Robinson, who left Earth aboard their Jupiter II spacecraft on a five-year voyage to explore a planet in the Alpha Centauri system, our nearest neighbor in the galaxy.
www.medialunchbox.com /ItemId/B0000DC3VM   (460 words)

  
 Lost In Space The Complete First Season DVD Review
Every week, “Lost In Space” fans tuned in to see how the Robinsons were going to get out of the last bit of trouble they’d run smack into, knowing full well that they’d be left on the edges of their seats waiting for the following week’s show.
When John slips free of the ship and starts to drift out into space, Maureen has to don a spacesuit and go after him, bringing the viewers to their first cliffhanger of the series, with the instructions to tune in to the “same time, same channel” next week.
Episode 19, “Ghost In Space,” features a return to straight comedy after a freak accident unleashes a disembodied presence that Dr. Smith believes is his uncle.
www.revolutionhometheater.com /dvd/revs/lost_in_space.shtml   (3276 words)

  
 Buy Complete Space & Astronomy by Topics Entertainment
Complete Space and Astronomy is the ultimate collector set and reference tool for students, home libraries, and space buffs.
Each title will stand alone as a complete educational program, and as a suite they are unmatched in content and value.
Included is a complete recreation of the flight of Apollo 13 using 3-D animation, original artwork, historic photos, video, and audio recordings.
www.e-dealsusa.com /2615.htm   (475 words)

  
 GameSpot:Video Games PC PlayStation 2 GameCube PSP DS GBA PS2 PS3 Xbox 360 PlayStation 3
Space Harrier is a behind-the-back shooter starring a flying man holding a large cannon.
With its bevy of options and complete look at Space Harrier on Sega's hardware, this one should be a nice treat for fans of the series, especially if those fans have already been burned by the rather weak remake of Space Harrier that was released last year.
Space Harrier Complete Collection is scheduled for a Japanese release in October.
www.gamespot.com /ps2/action/spaceharriercompletecollection/preview_6133699.html?part=rss&tag=gs_playstation_2&subj=6133699   (485 words)

  
 NASA - Space Shuttle
Engineers are moving closer to resolving the problem of large foam insulation falling off space shuttle external fuel tanks during launch.
NASA is using the May 3 to 23, 2006, launch window as a target for work to prepare Discovery for the mission.
Continued shuttle safety testing and a trip to the international space station are planned for the next space shuttle mission.
www.nasa.gov /mission_pages/shuttle/main/index.html   (327 words)

  
 Kids Domain - Review - Starry Night Complete Space & Astronomy Pack   (Site not responding. Last check: 2007-10-20)
Complete with the “Starry Night” cd-rom set, Deep Space Explorer disc, Skytheater DVD, and companion guide book, this program will teach you all you will ever need to know about the heavens.
The Deep Space Explorer disc has over an hour of video on topics relating to composition of the universe, fl holes, dark matter, and more.
This program is so complete and thorough, I doubt your junior or senior-high child would need anything else to learn astronomy.
www.kidsdomain.com /reviews/product.php?pid=1346   (377 words)

  
 Hilbert Space   (Site not responding. Last check: 2007-10-20)
As the example above shows, the space of rational numbers, with the usual notion of distance, is not a complete metric space.
is the completion of the space of continuous functions on the interval [a,b], with respect to a distance defined by
Therefore, the space of continuous functions is not complete.
jcbmac.chem.brown.edu /baird/QuantumPDF/Tan_on_Hilbert_Space.html   (1211 words)

  
 ESA Portal - Press Releases - Ariane 503/ARD : A successful complete European space mission   (Site not responding. Last check: 2007-10-20)
Europe has moved a step closer to flying its own complete space missions with the highly successful flight of an automatic capsule, the Atmospheric Reentry Demonstrator (ARD).
ARD was released during the Ariane 503 flight on 21 October, shortly after separation of the launcher's cryogenic main stage (at an altitude of about 216 km) 12 minutes after lift-off from the Guiana Space Centre, Europe's spaceport in Kourou, French Guiana.
For the first time ever Europe has flown a complete space mission - from launching a vehicle into space to recovering it safely.
www.esa.int /esaCP/Pr_46_1998_p_EN.html   (366 words)

  
 Complete Space and Astronomy Version 2.0 - from CDAccess.com
Space: A Visual History provides an archive of official, historical NASA film footage and photographs - see what the actual astronaut experience was like!
Complete Space and Astronomy Version 2 is by far the best product on the market with high quality software programs, and the reviews to prove it.
Through historical films and still photography, Space: A Visual History, chronicles the history of the US space program, from Alan Shepard's first launch in 1961, through the Skylab and Shuttle missions.
www.cdaccess.com /html/pc/space&a2.htm   (646 words)

  
 Atlantis astronauts complete tricky space station maneuver
The 27,000-pound beam, crammed with wiring and conduits, is the first of seven segments that will eventually become a 356-foot spine for the station that will support four giant solar-power arrays, heat radiators and new laboratory modules.
Astronauts from the space shuttle Atlantis, which docked with the station on Wednesday, completed one of their mission's most difficult tasks by attaching the truss to the station's Destiny science module.
They will deploy and attach two large tripod braces on the other side of the beam to complete its mechanical attachment to the station and continue mating electrical and fluid lines.
www.sfgate.com /cgi-bin/article.cgi?f=/c/a/2002/04/12/MN16371.DTL   (330 words)

  
 Computer Software Training - Computer Software :: Starry Night Complete Space & Astronomy Pack   (Site not responding. Last check: 2007-10-20)
When I saw that Children's Software Revue gave Starry Night Complete Space & Astronomy Pack 4.5 stars out of five and called it "the ideal package for either novice or expert astronomers who want to know a bit more about their backyard view of the universe," it was a must-buy for my household.
I knew SM Pro was more than she needed, so I got her the Complete Space & Astronomy Pack for her birthday and it fit the bill exactly.
Starry Night Complete Space & Astronomy Pack in particular will provide the budding astronomer with a wealth of stellar, planetary and other objects to fill a night's viewing -- and then some.
www.pctrainer.net /computer-software-training/B000227SUG/Starry_Night_Complete_Space_Astronomy_Pack.html   (755 words)

  
 CNN.com - Space - Astronauts complete space job despite equipment glitch - October 14, 2000
The short occurred as Wakata was preparing to latch onto the truss in the shuttle cargo bay and lift it onto the space station.
This is NASA's first space station construction mission since the initial components were launched in 1998.
It must be completed before the station's first permanent crew can lift off aboard a Russian rocket on October 30.
archives.cnn.com /2000/TECH/space/10/14/space.shuttle   (607 words)

  
 set cli complete-on-space   (Site not responding. Last check: 2007-10-20)
Configure the keys to use for command completion.
When you type a space or tab, the CLI performs command completion.
—Allow both a space and a tab to be used for command completion.
www.juniper.net /techpubs/software/junos/junos70/swcmdref70/html/cli-overview-cmdref37.html   (52 words)

  
 SpaceRef - Space News As It Happens
The camera was pointing toward Dione at approximately 38,352 kilometers away, and the image was taken using the CL1 and IR1 filters.
The discovery is another clue in solving a mystery: why the human immune system does not function well in the weightlessness of space.
NASA is set to approve development of 5 new unpressurized payload carriers for the Space Shuttle fleet at a total cost of $120 million.
www.spaceref.com   (804 words)

  
 Amazon.com: DVD: Lost in Space - The Complete First Season (1965)   (Site not responding. Last check: 2007-10-20)
I can still remember the horror and fascination of space in the mid-1960s, which at the time was completely new terrain.
Instead, you buy it because you want to remember how it was when you were 5 years old and you sat in your parents' living room, hunched over a fl-and-white TV set, scared out of your wits, yet thrilled to bits at the harrowing adventures of the Robinsons.
Lost in Space rarely, if at all, came close to the adventure and true danger shown in the first 5 episodes of season 1.
www.amazon.com /exec/obidos/tg/detail/-/B0000DC3VM?v=glance   (2738 words)

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