It tends to weakly Attractor | attracting Fixed_point_ ( mathematics ) | fixed point with multiplier = 0. 99993612384259

In mathematics, a function is weakly harmonic in a domain if

Thurston's geometrization conjecture, formulated in the late 1970s, offered a framework that suggested geometry and topology were closely intertwined in low dimensions, and Thurston's proof of geometrization for Haken manifolds utilized a variety of tools from previously only weakly linked areas of mathematics.

It tends to weakly Attractor | attracting Fixed point ( mathematics ) | fixed point with abs ( multiplier )= 0. 99993612384259

In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG ( i. e. a topological space for which all its homotopy groups are trivial ) by a free action of G. It has the property that any G principal bundle over a paracompact manifold is isomorphic to a pullback of the principal bundle

In mathematics, specifically in measure theory, a Borel measure is defined as follows: let X be a locally compact Hausdorff space, and let be the smallest σ-algebra that contains the open sets of X ; this is known as the σ-algebra of Borel sets.

In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.

The term compact was introduced into mathematics by Maurice Fréchet in 1906 as a distillation of this concept.

Some branches of mathematics such as algebraic geometry, typically influenced by the French school of Bourbaki, use the term quasi-compact for the general notion, and reserve the term compact for topological spaces that are both Hausdorff and quasi-compact.

In mathematics, compactification is the process or result of making a topological space compact.

Within mathematics, compact may refer to:

In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.

In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact.

In mathematics, a local field is a special type of field that is a locally compact topological field with respect to a non-discrete topology.

In mathematics, a trace class operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis.

In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface.

Closely related to this, in constructive mathematics, fewer characterisations of compact spaces are constructively valid — or from another point of view, there are several different concepts which are classically equivalent but not constructively equivalent.

In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π ( g ) is a unitary operator for every g ∈ G. The general theory is well-developed in case G is a locally compact ( Hausdorff ) topological group and the representations are strongly continuous.

In mathematics, G < sub > 2 </ sub > is the name of three simple Lie groups ( a complex form, a compact real form and a split real form ), their Lie algebras, as well as some algebraic groups.

In mathematics, the Peter – Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are not necessarily abelian.

In mathematics, a topological space is said to be σ-compact if it is the union of countably many compact subspaces.

In the mathematical fields of topology and K-theory, the Serre – Swan theorem, also called Swan's theorem, relates the geometric notion of vector bundles to the algebraic concept of projective modules and gives rise to a common intuition throughout mathematics: " projective modules over commutative rings are like vector bundles on compact spaces ".

In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact groups, such as R, the circle or finite cyclic groups.

In mathematics, the group algebra is any of various constructions to assign to a locally compact group an operator algebra ( or more generally a Banach algebra ), such that representations of the algebra are related to representations of the group.

In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary of a manifold.

In mathematics, especially in the area of abstract algebra known as module theory, algebraically compact modules, also called pure-injective modules, are modules that have a certain " nice " property which allows the solution of infinite systems of equations in the module by finitary means.

In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality ( size ) of sets.

Although Jevons predated the debate about ordinality or cardinality of utility, his mathematics required the use of cardinal utility functions.

In mathematics, a Mahlo cardinal is a certain kind of large cardinal number.

In mathematics, a Q-indescribable cardinal is a certain kind of large cardinal number that is hard to describe in some language Q.

In mathematics, a measurable cardinal is a certain kind of large cardinal number.

In mathematics, a cardinal number κ is called superstrong if and only if there exists an elementary embedding j: V → M from V into a transitive inner model M with critical point κ and ⊆ M.

In mathematics, a cardinal number κ is called huge if there exists an elementary embedding j: V → M from V into a transitive inner model M with critical point κ and

In the mathematics of transfinite numbers, an ineffable cardinal is a certain kind of large cardinal number, introduced by.

Many fields of mathematics bear the imprint of their creators for notation: the differential operator is due to Leibniz, the cardinal infinities to Georg Cantor ( in addition to the lemniscate (∞) of John Wallis ), the congruence symbol (≡) to Gauss, and so forth.

In set theory, a branch of mathematics, a rank-into-rank is a large cardinal λ satisfying one of the following four axioms ( commonly known as rank-into-rank embeddings, given in order of increasing consistency strength ):

In mathematics, under various anti-large cardinal assumptions, one can prove the existence of the canonical inner model, called the Core Model, that is, in a sense, maximal and approximates the structure of V. A covering lemma asserts that under the particular anti-large cardinal assumption, the Core Model exists and is maximal in a way.

In mathematics, a Ramsey cardinal is a certain kind of large cardinal number introduced by and named after Frank P. Ramsey.

In mathematics, an Erdős cardinal, also called a partition cardinal is a certain kind of large cardinal number introduced by.

In mathematics, subtle cardinals and ethereal cardinals are closely related kinds of large cardinal number.

In mathematics, limit cardinals are certain cardinal numbers.