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# Topic: Lebesgue covering dimension

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 Learn more about Dimension in the online encyclopedia.   (Site not responding. Last check: 2007-11-01) Dimension (from Latin "measured out") is, in essence, the number of degrees of freedom available for movement in a space. For any topological space, the Lebesgue covering dimension is defined to be n if any open cover has a refinement (a second cover where each element is a subset of an element in the first cover) such that no point is included in more than n+1 elements. The Krull dimension of a commutative ring is defined to be the maximal length of a strictly increasing chain of prime ideals in the ring. www.onlineencyclopedia.org /d/di/dimension.html   (669 words)

 Dimension - Facts, Information, and Encyclopedia Reference article In common usage, the dimensions of an object are the measurements that define its shape and size. In the physical sciences and in engineering, the dimension of a physical quantity is the expression of the class of physical unit that such a quantity is measured against. The Krull dimension of a commutative ring, named after Wolfgang Krull (1899 - 1971), is defined to be the maximal number of strict inclusions in an increasing chain of prime ideals in the ring. www.startsurfing.com /encyclopedia/d/i/m/Dimension.html   (1161 words)

 Dimension Time is frequently referred to as the "fourth dimension"; time is not the fourth dimension of space, but rather of spacetime. The theory of manifolds, in the field of geometric topology, is characterised by the way dimensions 1 and 2 are relatively elementary, the high-dimensional cases n'' > 4 are simplified by having extra space in which to 'work'; and the cases ''n = 3 and 4 are in some senses the most difficult. The Krull dimension of a commutative ring is defined to be the maximal number of strict inclusions in an increasing chain of prime ideals in the ring. www.nebulasearch.com /encyclopedia/article/Dimension.html   (590 words)

 PlanetMath: dimension The word dimension in mathematics has many definitions, but all of them are trying to quantify our intuition that, for example, a sheet of paper has somehow one less dimension than a stack of papers. One common way to define dimension is through some notion of a number of independent quantities needed to describe an element of an object. This is version 7 of dimension, born on 2003-10-18, modified 2004-03-29. planetmath.org /encyclopedia/Dimension3.html   (513 words)

 Dimension   (Site not responding. Last check: 2007-11-01) Also, in science fiction, a "dimension" can also refer to a separate world or plane of existence, though this meaning is not discussed in this article. It is somewhat different to the three spatial dimensions in that there is only one of it, and movement seems to be possible in only one direction. In physics, the dimension of a quality is the expression of that quality in basic units: the dimension of speed, for example, is length divided by time. www.freedownloadsoft.com /info/office-applications.html   (726 words)

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