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Encyclopedia > Compact

Compact as a general noun can refer to: Look up Compact on Wiktionary, the free dictionary

Compact is also the name of a 1960s British soap opera. Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. ... In mathematics, a compact space is a space that resembles a closed and bounded subset of Euclidean space Rn in that it is small in a certain sense and contains all its limit points. The modern general definition calls a topological space compact if every open cover of it has... In mathematics, a compact set is a set of points in a topological space such that every one of its (possibly infinite) open covers has a finite subcover. ... Jump to: navigation, search In mathematical logic the propositional calculus or sentential calculus is a formal deduction system whose atomic formulas are propositional variables. ... First-order predicate calculus or first-order logic (FOL) permits the formulation of quantified statements such as there exists an x such that. ... The compactness theorem is a basic fact in symbolic logic and model theory and asserts that a set (possibly infinite) of first-order sentences is satisfiable, i. ... Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering. ... Domain theory is a branch of mathematics that studies special kinds of partially ordered sets commonly called domains. ... In the mathematical area of order theory, the compact or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any directed set that does not already contain members above the compact element. ... Compact was a British television soap opera shown by the BBC between 1962 and 1965. ... Results from FactBites:

 Compact space - Wikipedia, the free encyclopedia (1379 words) 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 compact subset of a Hausdorff space is closed. Countably compact spaces are pseudocompact and weakly countably compact.
 Compact - Wikipedia, the free encyclopedia (192 words) Compact space, a closed and bounded subset of an Euclidean space. Compactness theorem, a set of first-order sentences is satisfiable if every finite subset of it is satisfiable. Compact element, those elements of a partially ordered set that cannot be subsumed by a supremum of any directed set that does not already contain them.
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