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1) "Compact" -- As to compact 1com·pact Pronunciation: k&m-'pakt, käm-', 'käm-" Function: adjective Etymology: Middle English, firmly put together, from Latin compactus, from past participle of compingere to put together, from com- + pangere to fasten -- more at PACT 1 : predominantly formed or filled : COMPOSED, MADE 2 a : having a dense structure or parts or units closely packed or joined <a compact woolen> <compact bone> b : not diffuse or verbose <a compact statement> c : occupying a small volume by reason of efficient use of space <a compact camera> <a compact formation of troops> d : short-bodied, solid, and without excess flesh 3 : being a topological space and especially a metric space with the property that for any collection of open sets which contains it there is a subset of the collection with a finite number of elements which also contains it - com·pact·ly /-'pak(t)-lE, -"pak(t)-/ adverb - com·pact·ness /-'pak(t)-n&s, -"pak(t)-/ noun Pronunciation Symbols In mathematics, a subset of Euclidean space Rn is called compact if it is closed and bounded. For example, in R, the closed unit interval [0, 1] is compact, but the set of integers Z is not (it is not bounded) and neither is the half-open interval [0, 1) (it is not closed). A more modern approach is to call a topological space compact if each of its open covers has a finite subcover. The Heine–Borel theorem shows that this definition is equivalent to "closed and bounded" for subsets of Euclidean space. Note: Some authors such as Bourbaki use the term "quasi-compact" instead and reserve the name "compact" for topological spaces that are Hausdorff and compact. 1 History and motivation 2 Definitions 2.1 Compactness of subsets of Rn 2.2 Compactness of topological spaces 3 Examples of compact spaces 4 Theorems 5 Other forms of compactness 6 See also 7 References The term compact was introduced by Fréchet in 1906. It has long been recognized that a property like compactness is necessary to prove many useful theorems. It used to be that "compact" meant "sequentially compact" (every sequence has a convergent subsequence). This was when primarily metric spaces were studied. The "covering compact" definition has become more prominent because it allows us to consider general topological spaces, and many of the old results about metric spaces can be generalized to this setting. This generalization is particularly useful in the study of function spaces, many of which are not metric spaces. One of the main reasons for studying compact spaces is because they are in some ways very similar to finite sets: there are many results which are easy to show for finite sets, whose proofs carry over with minimal change to compact spa..." Further Data On Term for compact Internet users who seek compact often also seach for: kitchen trash compactors, compact cd, gb compact flash, compact pc, compact flash usb, self compacting concrete, danby compact refrigerator, compact pro, compact tractor, recordable compact disc, compactflash, reader, compact, tripod, compact, stereos, 128, mb, compact, flash, card, 128, mb, compact, flash, 1, gb, compact, flash, compaction, grouting, compact, refrigerators, broan, trash, compactors, 128mb, compact, flash, kitchen, trash, compactors, compact, cd, gb, compact, flash, compact, pc, compact, flash, usb, self, compacting, concrete, danby, compact, refrigerator, compact, pro, compact, tractor, recordable, compact, disc Regularly Occuring Typos with compact include: ocmpact cmopact copmact comapct compcat compatc ompact cmpact copact comact compct compat compac xompact dompact fompact vompact kompact cimpact ckmpact clmpact cpmpact campact cempact cumpact conpact cojpact cokpact comoact compqct compsct compzct compect compict compoct compuct compaxt compadt compaft compavt compakt compacr compacf compacg compacy Commonly appearing connections are : component, complete solution, compatibility tests, compare to, compare cost of living, compaq presario notebook 1200, compaq armada 3500, compact flash rebate, compact flash ii, compact dishwasher, compact disc recordable, commercial blender, comic book sleeves, comforters, combi twin savvy, combi strollers, combi double stroller, com spy, colusa real estate, columns, columbia video, columbia river sturgeon fishing Similar searches have yielded these phrases compact: compactflash reader, compact tripod, compact stereos, 128 mb compact flash card, 128 mb compact flash, 1 gb compact flash, compaction grouting, compact refrigerators, broan trash compactors, 128mb compact flash Certain copy here compact made available through Wikipedia and the GNU Free Documentation License.