branches of mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair of distinct points of...

interpretation Kolmogorov microscales Kolmogorov's normability criterion Fréchet–Kolmogorov theorem Kolmogorov space Kolmogorov complexity Kolmogorov–Smirnov...

T3 if and only if it is both regular and T0. (A T0 or Kolmogorov space is a topological space in which any two distinct points are topologically distinguishable...

product space Kolmogorov space Lp-space Lens space Liouville space Locally finite space Loop space Lorentz space Mapping space Measure space Metric space Minkowski...

topological space. Moreover, for a uniformizable space X {\displaystyle X} the following are equivalent: X {\displaystyle X} is a Kolmogorov space X {\displaystyle...

meaning.) A topological space is a T1 space if and only if it is both an R0 space and a Kolmogorov (or T0) space (i.e., a space in which distinct points...

distinguishable). A topological space is preregular if and only if its Kolmogorov quotient is Hausdorff. For a topological space X {\displaystyle X} , the following...

In probability theory, Kolmogorov equations characterize continuous-time Markov processes. In particular, they describe how the probability of a continuous-time...

In statistics, the Kolmogorov–Smirnov test (also K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section...

foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to...

is always a Kolmogorov space (i.e., it satisfies the T0 separation axiom). However, a dcpo with the Scott topology is a Hausdorff space if and only if...

Remark. Completely regular spaces and Tychonoff spaces are related through the notion of Kolmogorov equivalence. A topological space is Tychonoff if and only...

of Markovian stochastic processes in probability theory, the Chapman–Kolmogorov equation (CKE) is an identity relating the joint probability distributions...

In probability theory, Kolmogorov's zero–one law, named in honor of Andrey Nikolaevich Kolmogorov, specifies that a certain type of event, namely a tail...

Taking Kolmogorov quotients, we see that all normal T1 spaces are Tychonoff. These are what we usually call normal Hausdorff spaces. A topological space is...

In fluid dynamics, Kolmogorov microscales are the smallest scales in turbulent flow. At the Kolmogorov scale, viscosity dominates and the turbulence kinetic...

The following theorem is due to Kolmogorov: Kolmogorov's normability criterion: A Hausdorff topological vector space is normable if and only if there...

information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest...

to that event. The Soviet mathematician Andrey Kolmogorov introduced the notion of a probability space and the axioms of probability in the 1930s. In...

In mathematics, a Hilbert space is a real or complex inner product space that is also a complete metric space with respect to the metric induced by the...

mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem)...

The Kolmogorov–Arnold–Moser (KAM) theorem is a result in dynamical systems about the persistence of quasiperiodic motions under small perturbations. The...

T0 or T00 may refer to: T0 space, a Kolmogorov space T0, a level on the tornado TORRO scale T−0, the end of a rocket's launch countdown and the beginning...

In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous...

mathematics, Fisher-KPP equation (named after Ronald Fisher , Andrey Kolmogorov, Ivan Petrovsky, and Nikolai Piskunov) also known as the Fisher equation...

In probability theory, the Borel–Kolmogorov paradox (sometimes known as Borel's paradox) is a paradox relating to conditional probability with respect...

topologists' terms: Weil's idea fails to give a Kolmogorov space and Zariski thinks in terms of the Kolmogorov quotient.) In the rapid foundational changes...

 262. hdl:2027/mdp.49015000696204. Cf. definition 39.7 and lemma 39.8. Kolmogorov, A. N.; Fomin, S. V. (1957) [1954]. Elements of the theory of functions...

{C}}(a,b)} is called the uniform norm or supremum norm ('sup norm'). Kolmogorov, A. N., & Fomin, S. V. (1967). Elements of the theory of functions and...

points. Hence X {\displaystyle X} is not a Kolmogorov space, nor a T1 space, a Hausdorff space or an Urysohn space. In a partition topology the complement...