Many theorems which are provable using choice are of an elegant general character: every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact.

Many agates are hollow, since deposition has not proceeded far enough to fill the cavity, and in such cases the last deposit commonly consists of drusy quartz, sometimes amethystine, having the apices of the crystals directed towards the free space so as to form a crystal-lined cavity or geode.

Many GA-style guitars also have a convex back panel to increase the volume of space in the soundbox without making the soundbox deeper at the edges, which would affect comfort and playability.

Many Greek sculptures followed, notably the first purpose-built exhibition space, the Charles Towneley collection, much of it Roman Sculpture, in 1805.

Many contemporary thinkers actually suggest that time is the fourth dimension, thus reducing space and time to one distinct ontological entity, the space-time continuum.

** Many embedded applications have a limited amount of physical space for circuitry ; keeping peripherals on-chip will reduce the space required for the circuit board.

Many other coordinate systems have been developed since Descartes, such as the polar coordinates for the plane, and the spherical and cylindrical coordinates for three-dimensional space.

Many of the successful programs were transitioned to the Services, such as the foundation technologies in automatic target recognition, space based sensing, propulsion, and materials that were transferred to the Strategic Defense Initiative Organization ( SDIO ), later known as the Ballistic Missile Defense Organization ( BMDO ), now titled the Missile Defense Agency ( MDA ).

( Many authors refer to R < sup > n </ sup > itself as Euclidean space, with the Euclidean structure being understood ).

Many CPU architectures instead use so-called memory mapped I / O, in which a common address space is used for both RAM and peripheral chips.

Many of her stories have a milieu reminiscent of the space opera and pulp tales she read in her youth, but typically with a much darker tone: the cosmic journeys of her characters are often linked to a drastic spiritual alienation, and / or a transcendent experience which brings fulfillment but also death.

Many maps are static two-dimensional, geometrically accurate ( or approximately accurate ) representations of three-dimensional space, while others are dynamic or interactive, even three-dimensional.

Many space observatories have already completed their missions, while others continue operating, and still others are planned for the future.

Many of these are essentially straightforward newspapers, publishing in tabloid format, because subway and bus commuters prefer to read smaller-size newspapers due to lack of space.

Many explorers find decay of uninhabited space to be profoundly beautiful and some are also proficient freelance photographers.

Many processors also use tree representations that are significantly more efficient ( in both space and time ) than general-purpose DOM implementations.

Many arabesque patterns disappear at ( or " under " as it often appears to a viewer ) a framing edge without ending, and thus can be regarded as infinitely extendable outside the space they actually occupy ; this was certainly a distinctive feature of the Islamic form, though not without precedent.

Many fundamental physical laws are mathematical consequences of various symmetries of space, time, or other aspects of nature.

Many of his works incorporated optical illusions, negative space, visual puns, and trompe l ' oeil visual effects.

Many such companies are large, and are able to have a smaller space available to workshop an experimental production or present playreadings.

Many space missions are more suited to telerobotic rather than crewed operation, due to lower cost and lower risk factors.

Many questions are asked about the origins and mission of the aliens, but they avoid answering, preferring to remain in their space ships, governing through indirect rule.

Many elements of space travel series and films borrow extensively from the conventions of the Western genre.

Many people think that pansies last only a few weeks, then their period of growth and bloom is over.

Many scholars consider modern anthropology as an outgrowth of the Age of Enlightenment, a period when Europeans attempted to study human behavior systematically, the known varieties of which had been increasing since the fifteenth century as a result of the first European colonization wave.

Many batting records were set in this period.

Many Jews consider a portion of the 49-day period of the counting of the omer between Passover and Shavuot to be a time of semi-mourning and instrumental music is not allowed during that time.

Many downtown buildings ( about 5, 000 ), including those on the quays, are from this period.

Many city-states in ancient Greece limited debt slavery to a period of five years and debt slaves had protection of life and limb, which regular slaves did not enjoy.

Many notable sea canals were completed in this period, starting with the Suez Canal ( 1869 )-which carries tonnage many times that of most other canals-and the Kiel Canal ( 1897 ), though the Panama Canal was not opened until 1914.

Many amillennialists believe that during this time period, the church will continue to evangelize and grow as well as suffer declination in periods until Christ ’ s coming.

Many cruisers are " long term " and travel for many years, the most adventurous among them circle the globe over a period of three to ten years.

Many groups that were popular during the disco period subsequently struggled to maintain their success — even those that tried to adapt to evolving musical tastes.

Many Protestant congregations generally reserve a period of time for self-examination and private, silent confession just before partaking in the Lord's Supper.

Many of these trivial errors occurred in the Byzantine period, following a change in script from uncial to minuscule, and many were ' homophonic ' errors, when scribes accidentally substituted homophones for words in the textequivalent in English to substituting ' right ' for ' write ', except that there were more opportunities for Byzantine scribes to make these errors because the Greek letters η, ι, οι and ει were pronounced similarly in the Byzantine period.

Many of these Volunteers were arrested in the period following the rising, while others, including Mellows had to go " on the run " to escape.

Many of the German films of the immediate post-war period can be characterised as belonging to the genre of the Trümmerfilm ( literally " rubble film ").

Many pictures released from the 1960s onward share attributes with film noir of the classical period, and often treat its conventions self-referentially.

Many other Republicans remained in exile for the entire Franco period.

Many Albanians converted to the Roman Catholic Church at that period.

Many Confucian-educated Chinese who now lacked profession turned to the arts of painting and theatre instead, as the Yuan period became one of the most vibrant and abundant eras for Chinese artwork.

Many suggest that during the First Temple period, the people of Israel believed that each nation had its own god, but that their god was superior to other gods.

Many deaths in the late 19th and early 20th century period were attributed to rescue teams being unable to locate those that had become lost in snowy regions as they were wearing only white.

Many ancient murals have survived in Egyptian tombs ( around 3150 BC ), the Minoan palaces ( Middle period III of the Neopalatial period, 1700-1600 BC ) and in Pompeii ( around 100 BC-AD 79 ).

Many of the city's finest buildings belong to this period and were built under the first three Bavarian kings.

Many variants of mahjong developed during this period.