Tightness may refer to:
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In mathematics, tightness is a concept in measure theory. The intuitive idea is that a given collection of measures does not "escape to infinity."
In mathematics, a cardinal function is a function that returns cardinal numbers.
Tightness is defined as a point in time where economically, it is very difficult to invest, but it is far easier to sell or to remove investments in return of monetary rewards. The higher the level of the tightness, the more expensive, less common, and less reliable the market becomes. For example, during the late 1990s technology boom in the West, Information Technology companies were very difficult and expensive to buy a part of, through stock, loan, or other methods, due to the tightness of competition in the market.
In other fields,
In physics, tension may be described as the pulling force transmitted axially by the means of a string, cable, chain, or similar one-dimensional continuous object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements. Tension could be the opposite of compression.
In physics and engineering, permeation is the penetration of a permeate through a solid. It is directly related to the concentration gradient of the permeate, a material's intrinsic permeability, and the materials' mass diffusivity. Permeation is modeled by equations such as Fick's laws of diffusion, and can be measured using tools such as a minipermeameter.
A miser is a person who is reluctant to spend, sometimes to the point of forgoing even basic comforts and some necessities, in order to hoard money or other possessions. Although the word is sometimes used loosely to characterise anyone who is mean with their money, if such behaviour is not accompanied by taking delight in what is saved, it is not properly miserly.
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A knot is an intentional complication in cordage which may be useful or decorative. Practical knots may be classified as hitches, bends, splices, or knots. A hitch fastens a rope to another object; a bend unites two rope ends; a splice is a multi-strand bend or loop. A knot in the strictest sense serves as a stopper or knob at the end of a rope to keep that end from slipping through a grommet or eye. Knots have excited interest since ancient times for their practical uses, as well as their topological intricacy, studied in the area of mathematics known as knot theory.
In mathematics, topology is concerned with the properties of space that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing.
The overhand knot is one of the most fundamental knots, and it forms the basis of many others, including the simple noose, overhand loop, angler's loop, reef knot, fisherman's knot, and water knot. The overhand knot is a stopper, especially when used alone, and hence it is very secure, to the point of jamming badly. It should be used if the knot is intended to be permanent. It is often used to prevent the end of a rope from unraveling. An overhand knot becomes a trefoil knot, a true knot in the mathematical sense, by joining the ends.
In mathematics, and more specifically in topology, an open set is an abstract concept generalizing the idea of an open interval in the real line. The simplest example is in metric spaces, where open sets can be defined as those sets which contain a ball around each of their points ; however, an open set, in general, can be very abstract: any collection of sets can be called open, as long as the union of an arbitrary number of open sets is open, the intersection of a finite number of open sets is open, and the space itself is open. These conditions are very loose, and they allow enormous flexibility in the choice of open sets. In the two extremes, every set can be open, or no set can be open but the space itself and the empty set.
In mathematics, the real line, or real number line is the line whose points are the real numbers. That is, the real line is the set R of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one. It can be thought of as a vector space, a metric space, a topological space, a measure space, or a linear continuum.
In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively studied by Polish topologists and logicians—Sierpiński, Kuratowski, Tarski and others. However, Polish spaces are mostly studied today because they are the primary setting for descriptive set theory, including the study of Borel equivalence relations. Polish spaces are also a convenient setting for more advanced measure theory, in particular in probability theory.
Uniformity may refer to:
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A = A(K) of K. It consists of the points of G having values in A; the definition of the appropriate topology is straightforward only in case G is a linear algebraic group. In the case of G being an abelian variety, it presents a technical obstacle, though it is known that the concept is potentially useful in connection with Tamagawa numbers. Adelic algebraic groups are widely used in number theory, particularly for the theory of automorphic representations, and the arithmetic of quadratic forms.
Mathematics encompasses a growing variety and depth of subjects over history, and comprehension requires a system to categorize and organize the many subjects into more general areas of mathematics. A number of different classification schemes have arisen, and though they share some similarities, there are differences due in part to the different purposes they serve. In addition, as mathematics continues to be developed, these classification schemes must change as well to account for newly created areas or newly discovered links between different areas. Classification is made more difficult by some subjects, often the most active, which straddle the boundary between different areas.
In mathematics, a structure on a set is an additional mathematical object that, in some manner, attaches to that set to endow it with some additional meaning or significance.
In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independent of Zermelo–Fraenkel set theory (ZFC).
In mathematics, a space is a set with some added structure.
In mathematics, an inner regular measure is one for which the measure of a set can be approximated from within by compact subsets.
In mathematics, classical Wiener space is the collection of all continuous functions on a given domain, taking values in a metric space. Classical Wiener space is useful in the study of stochastic processes whose sample paths are continuous functions. It is named after the American mathematician Norbert Wiener.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line. The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2. Included within the irrationals are the transcendental numbers, such as π (3.14159265...). In addition to measuring distance, real numbers can be used to measure quantities such as time, mass, energy, velocity, and many more.
This is a glossary of terms that are or have been considered areas of study in mathematics.