Page "Axiom of choice" ¶ 57
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## Some Related Sentences

** and Hausdorff
** The Hausdorff paradox.
** CmptH, the category of all compact Hausdorff spaces
** Hausdorff topologies are better-behaved than those in arbitrary general topology.
** Hausdorff dimension

** and maximal
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** Antichain principle: Every partially ordered set has a maximal antichain.
** Every unital ring other than the trivial ring contains a maximal ideal.
** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.
** Referring to diplomas and degrees: cum laude ( with praise ), magna cum laude ( with great praise ); maxima cum laude ( with maximal praise ); summa cum laude ( with highest praise ); egregia cum laude ( with outstanding praise )
** Find all maximal pairs, maximal repeats or supermaximal repeats in time.
** Maximal planar graphs are sometimes called triangulations, and a maximal planar supergraph of a graph G may be called a triangulation of G.
** These two concepts come together in strangulated graphs, which include both maximal planar graphs and chordal graphs.

** and principle
** Microevolution: species — speciation — adaptation — selection — natural selection — directional selection — sexual selection — genetic drift — sexual reproduction — asexual reproduction — colony — allele frequency — neutral theory of molecular evolution — population genetics — Hardy-Weinberg principle
** to the greatest benefit of the least advantaged, consistent with the just savings principle, and
** The segmented DAC, which combines the thermometer-coded principle for the most significant bits and the binary-weighted principle for the least significant bits.
** " Uncertainty principle " -- Jan Hilgevoord and Jos Uffink.
** In the mid-1950s, a second land reform during the Great Leap Forward compelled individual farmers to join collectives, which, in turn, were grouped into People's communes with centrally controlled property rights and an egalitarian principle of distribution.
** Li ( Neo-Confucianism ), philosophical concept of principle
** Some, including the leadership of the Society of St Pius X, hold that it is in principle valid as a sacramental rite but maintain that the revisions in the liturgy are displeasing to God, and that it is often celebrated improperly to the extent of being sacramentally invalid.
** Some, including many sedevacantists, see it as categorically invalid in principle and entirely unacceptable.
** Blackstone's formulation, a principle in criminal law named for the jurist
** Duality ( projective geometry ), general principle of projective geometry
** Morton's fork coup, a technique in the game of Bridge that uses the principle of Morton's Fork
** What are ( necessary and sufficient ) conditions for consistency of a learning process based on the empirical risk minimization principle?
** A-Frame house, a house following the same principle
** Adage, a principle in the form of a memorable saying
** Legal analyses on the principle of laïcité ( decisions and opinions of the Conseil d ' État )
** Equivalence principle
** ( 1949 ): Human behavior and the principle of least effort
** Sigmund Freud's will to pleasurepleasure principle
** Stalin ordered that the persecution be enhanced: NKVD is " four years late " in crushing the opposition, according to his principle of " aggravation of class struggle "
** Specific amorality, the absence of some particular moral standard, principle, code, or knowledge
** the Government decision of December 2002 to agree in principle to the provision of additional resources was made contingent on the outcome of the review, and so had proved meaningless.
** T31 / M5A2-Similar in principle to the M3A2, a vehicle developed by the US Ordnance Department to combine the production of the M5 and M9 into a single vehicle.

** and any
** The Cartesian product of any family of nonempty sets is nonempty.
** The Serbians use word " cifra ", which refers to any number. Besides " cifra ", they use word " broj ".
** In particular, the cofinality of any nonzero finite ordinal, or indeed any finite directed set, is 1, since such sets have a greatest element.
** In power engineering, a " bus " is any graph node of the single-line diagram at which voltage, current, power flow, or other quantities are to be evaluated.
** BAFTA Film Award nomination for Best Film from any Source
** Informally, any GPS navigation device, especially an automotive navigation system
** Kosher style, food made with a kosher appearance but without any claim to be kosher
** binary – any sequence of octets.
** Oceanids ( daughters of Oceanus and Tethys, any water, usually salty )
** Old Believings It was believed that in England in the 14th century, that plains of any kind is where the dead wandered searching for their revenge.
** This could be any position in which the speaker — whether an acknowledged expert on the subject, or an acquaintance of a person who experienced the matter in question — knows about the topic.
** Sodium chloride ( table salt ) or any other salt in water forms an electrolyte: When dissolving, salt dissociates into ions.
** In the UK, a protective trust is a life interest which terminates on the happening of a specified event such as the bankruptcy of the beneficiary or any attempt by him to dispose of his interest.
** Note: Patient may die before any symptoms appear
** San Francisco elects City Supervisor Harvey Milk, the first openly gay elected official of any large city in the U. S.
** British Prime Minister Neville Chamberlain states in the House of Commons that any German attack on France will be automatically considered an attack on Britain.
** The Western Allies flatly reject any offer of surrender by Germany other than unconditional on all fronts.
** American Civil War: The U. S. House unanimously passes a resolution guaranteeing non-interference with slavery in any state.
** A decision by the Supreme Court of the United States states that the power of the federal government is greater than any individual state.
** The Naval Defence Act dictates that the fleet strength of the British Royal Navy must be equal to that of at least any two other countries.
** Pakistan Navy raids Indian coasts without any resistance in Operation Dwarka, Pakistan celebrates Victory Day annually.
** Brisbane receives a daily rainfall of 465 millimetres – a record for any Australian capital city.
** Pen Hadow becomes the first person to walk alone, without any outside help, from Canada to the North Pole.

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