** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

In general topological spaces, however, the different notions of compactness are not necessarily equivalent, and the most useful notion, introduced by Pavel Alexandrov and Pavel Urysohn in 1929, involves the existence of certain finite families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.

In general topological spaces, however, the different notions of compactness are not equivalent, and the most useful notion of compactness — originally called bicompactness — involves families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.

Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.

* The cofinality of a partially ordered set with greatest element is 1 as the set consisting only of the greatest element is cofinal ( and must be contained in every other cofinal subset ).

The halves contained the same set of data and were identical, except the upper half had two holes for a string or twine to go through.

During the 1880s, five foreign editions contained two revelations to John Taylor that were received in 1882 and 1883 ; these revelations " set in order " the priesthood, gave more clarification about the roles of priesthood offices — especially the Seventy — and required Priesthood leaders to live plural marriage in order to qualify to hold their church positions.

Before the entry into force of Protocol 11, Section II ( Article 19 ) set up the Commission and the Court, Sections III ( Articles 20 to 37 ) and IV ( Articles 38 to 59 ) included the high-level machinery for the operation of, respectively, the Commission and the Court, and Section V contained various concluding provisions.

It states that in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

The Hausdorff maximal principle states that, in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

There was also a boxed set called variously The Factory Set and One With Everything which contained one of each card from the main set of the limited edition, multiples of the Illuminati cards, and a few cards previously only available in magazines.

The London Regional Transport Act contained provision for setting up subsidiary companies to run the Underground and bus services and in 1985 London Underground Limited ( LUL ), a wholly owned subsidiary of London Regional Transport, was set up to manage the tube network.

A measure can be extended to a complete one by considering the σ-algebra of subsets Y which differ by a negligible set from a measurable set X, that is, such that the symmetric difference of X and Y is contained in a null set.

Then N < sub > x </ sub > is a directed set, where the direction is given by reverse inclusion, so that S ≥ T if and only if S is contained in T. For S in N < sub > x </ sub >, let x < sub > S </ sub > be a point in S. Then ( x < sub > S </ sub >) is a net.

In addition to two or three alliterations, the odd numbered lines had partial rhyme of consonants with dissimilar vowels, not necessarily at the beginning of the word ; the even lines contained internal rhyme in set syllables ( not necessarily at the end of the word ).

He kept out of Epistolae familiares a special set of 19 controversial letters called Liber sine nomine that contained much criticism of the Avignon papacy.

The LSI-11 ( PDP-11 / 03 ), introduced in February, 1975 was the first PDP-11 model produced using large-scale integration ; the entire CPU was contained on four LSI chips made by Western Digital ( the MCP-1600 chip set ; a fifth chip could be added to extend the instruction set, as pictured on the right ).

* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.

Initially set up under the HVP as a rocket training battery ( Number 444 ), Heimat-Artillerie-Park 11 Karlshagen / Pomerania ( HAP 11 ) also contained the A-A Research Command North for the testing of anti-aircraft rockets.

Later in 1979, Sony and Philips set up a joint task force of engineers to design a new digital audio disc.

Throughout the 1980s and ' 90s, Young promised fans a follow-up to the original Decade collection, provisionally titled Decade II ; eventually, this idea was scrapped in favor of a much more comprehensive anthology to be titled Archives, spanning his entire career and ranging in size from a box set to an entire series of audio and / or video releases.

The Davros Mission is an original audio adventure ( without the Doctor ) available on the Complete Davros Collection DVD box set.

By the time of the Eighth Doctor audio play Terror Firma ( set after Remembrance ), Davros is commanding a Dalek army which has successfully conquered the Earth.

Another version is the Collector's Edition, a two-disc set featuring a remastered transfer with a 5. 1 audio track, two commentaries ( one by John Carpenter and Kurt Russell, another by producer Debra Hill and Joe Alves ), a making-of featurette, the first issue of a comic book series titled John Carpenter's Snake Plissken Chronicles, and a ten-minute deleted opening sequence.

For example, a key frame could be set to indicate the point at which audio will have faded up or down to a certain level.

MIDI carries note event messages that specify notation, pitch and velocity, control signals for parameters such as volume, vibrato, audio panning and cues, and clock signals that set and synchronize tempo between multiple devices.

Because MIDI is a set of commands that create sound, MIDI sequences can be manipulated in ways that prerecorded audio cannot.

A MIDI file is in no way a recording of actual music, it is a spreadsheet-like set of instructions, and can use a thousand times less disk space than the equivalent recorded audio.

The Moving Picture Experts Group ( MPEG ) is a working group of experts that was formed by ISO and IEC to set standards for audio and video compression and transmission.

In 1999, Brøderbund / The Learning Company released Totally Mad, a Microsoft Windows 95 / 98 compatible CD-ROM set collecting the magazine's content from # 1 through # 376 ( December 1998 ), plus over 100 Mad Specials including most of the recorded audio inserts.

The Xiph. Org Foundation decided to create a new set of file extensions and media types to describe different types of content such as. oga for audio only files,. ogv for video with or without sound ( including Theora ), and. ogx for multiplexed Ogg.

Most commonly it is used to control video output, but it can write to most of the chipset registers and thus can be used to set audio registers or interrupt the CPU.

A software technique was later developed which can play back 14-bit audio by combining two channels set at different volumes.

* A parametric equaliser is an audio filter that allows the frequency of maximum cut or boost to be set by one control, and the size of the cut or boost by another.

In early November 2005, Staind released the limited edition 2-CD / DVD set of Chapter V. The set included several rarities and fan favorites — music videos ; a complete, 36-page booklet with exclusive artwork ; an audio disc with an acoustic rendition of " This is Beetle "; the original, melodic rendition of " Reply "; the previously released B-side singles " Novocaine " and " Let It Out "; and live versions of " It's Been Awhile " and " Falling ", among many others.

Consumer equipment, and in particular compact audio cassette recorders have the bias set at a compromise level ( usually a little higher ) to give good frequency response and acceptably low distortion.

A website, also written as Web site, web site, or simply site, is a set of related web pages containing content such as text, images, video, audio, etc.

The museum is set in gardens, which include full-sized reconstructions of a Roman temple, a Roman shop, Roman house and Northumbrian croft, all with audio presentations.

Also, data drives can only read or write audio MDs when set in " play " mode, which, however, does not provide computer access to the data.

Usually there was a scanner or camera, a modem to create and receive the characteristic audio howl, and a cathode ray tube from a surplus radar set.

The song plays live on a never-ending audio stream on a special web site set up by the band and was made available for purchase as a hard drive encased in an actual human skull, limited to 13 copies.

* The Doctor Who audio drama Loups-Garoux is set in Brazil in 2080.