# compactness

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**Fixed point (mathematics)**— Not to be confused with a stationary point where f (x) = 0. A function with three fixed points In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is a point[1] that is …92

**Saturated model**— There is an unrelated notion of saturated model in the context of structural equation modeling. In mathematical logic, and particularly in its subfield model theory, a saturated model M is one which realizes as many complete types as may be… …93

**Compact operator**— In functional analysis, a branch of mathematics, a compact operator is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset of Y. Such an… …94

**Arzelà–Ascoli theorem**— In mathematics, the Arzelà–Ascoli theorem of functional analysis gives necessary and sufficient conditions to decide whether every subsequence of a given sequence of real valued continuous functions defined on a closed and bounded interval has a… …95

**Compact element**— 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 non empty directed set that does not already contain members above the compact… …96

**Semilattice**— In mathematics, a join semilattice (or upper semilattice) is a partially ordered set which has a join (a least upper bound) for any nonempty finite subset. Dually, a meet semilattice (or lower semilattice) is a partially ordered set which has a… …97

**First-countable space**— In topology, a branch of mathematics, a first countable space is a topological space satisfying the first axiom of countability . Specifically, a space, X , is said to be first countable if each point has a countable neighbourhood basis (local… …98

**Lab-on-a-chip**— This article is about the technology. For the journal, see Lab on a Chip (journal). Lab on a chip made of glass A lab on a chip (LOC) is a device that integrates one or several laboratory functions on a single chip of only millimeters to a few… …99

**Helly's theorem**— In geometry, Helly s theorem is a basic combinatorial result on convex sets. It was proved by Eduard Helly in 1923, and gave rise to the notion of Helly family.tatement of Helly s theorem:Suppose that::X 1,X 2,dots,X n :is a finite collection of… …100

**PMODE**— is a DOS extender used in several IBM PC compatible DOS applications in the mid and late 1990s. It was created by Thomas Tran Pytel, and the first version became publicly available in 1994. The original PMODE was written to be used with programs… …