$#A+1 = 25 n = 0
$#C+1 = 25 : ~/encyclopedia/old_files/data/H047/H.0407520 Holomorph of a group
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$#A+1 = 22 n = 0
$#C+1 = 22 : ~/encyclopedia/old_files/data/C021/C.0201440 Channel with a finite memory
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$#A+1 = 97 n = 0
...= 97 : ~/encyclopedia/old_files/data/G044/G.0404910 Graph, connectivity of a
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''of a set $A$ in a [[topological space]] $X$''
...$x$. The interior may be denoted $A^\circ$, $\mathrm{Int} A$ or $\langle A \rangle$.
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...,b \in A$, $aRb$ implies $b R a$, i.e. $R \subseteq R^{-1}$. An example of a symmetric relation is an [[Equivalence relation]].
...n $R$ such that $R \cap R^{-1} \subseteq \Delta = \{ (x,x) : \forall x \in A \}$.
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$#A+1 = 43 n = 0
$#C+1 = 43 : ~/encyclopedia/old_files/data/F040/F.0400660 Flow in a network
7 KB (1,074 words) - 20:15, 15 March 2023
$#A+1 = 29 n = 0
$#C+1 = 29 : ~/encyclopedia/old_files/data/C024/C.0204560 Conductor of a character
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$#A+1 = 20 n = 0
$#C+1 = 20 : ~/encyclopedia/old_files/data/E036/E.0306850 Exhaustion of a domain,
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...e also the [[Borel set|Borel sets]]) and $\mu: \mathcal{B}\to [0, \infty]$ a ($\sigma$-additive) measure (cp. with [[Borel measure]]). The support of $\
The existence of a countable base guarantees that
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''$A$ in a topological space $X$''
The intersection of all [[closed set]]s of $X$ containing the set $A$.
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$#A+1 = 5 n = 0
$#C+1 = 5 : ~/encyclopedia/old_files/data/O068/O.0608030 Object in a category
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''(general and special rank of a group)''
...is the minimal number such that any finitely-generated subgroup of $G$ has a system of generators of at most $r$ elements. If no such finite number exis
1 KB (182 words) - 16:24, 19 April 2014
...the triangle with the midpoint of the opposite side. The three medians of a triangle intersect at one point, called the centre of gravity, the [[centro
...] (cf. [[Lobachevskii geometry]]) the meridians of a triangle intersect at a point.
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...e $X$ is said to be of the first category in $X$ if it can be expressed as a finite or countable union of [[nowhere-dense set|nowhere dense sets]] in $X
...h sets is residual (or comeager), cp. again with Chapter 9 of {{Cite|Ox}}. A non-empty closed set of real numbers, in particular an interval, is not of
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#REDIRECT [[Interior of a set]]
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...and its deformation $F^*$ outside their points of congruence. The base of a deformation is characterized by the fact that the bend — the relation bet
...<TD valign="top"> V.F. Kagan, "Foundations of the theory of surfaces in a tensor setting" , '''2''' , Moscow-Leningrad (1948) (In Russian)</TD></TR
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A concept of classical measure theory generalized further in [[Geometric meas
===Lebesgue density of a set===
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...encyclopediaofmath.org/legacyimages/m/m063/m063460/m0634601.png" /> (or on
a Riemann surface <img align="absmiddle" border="0" src="https://www.encyclop
...ww.encyclopediaofmath.org/legacyimages/m/m063/m063460/m06346010.png" /> is
a field with respect to the usual [[pointwise operation]]s followed by redefi
44 KB (5,974 words) - 22:47, 29 November 2014
$#A+1 = 5 n = 0
...deformation]] of a surface. It is the set of points in space described by a position vector $ \mathbf y $
2 KB (294 words) - 06:37, 9 April 2023
...the triangle with the midpoint of the opposite side. The three medians of a triangle intersect at one point, called the centre of gravity, the [[centro
...] (cf. [[Lobachevskii geometry]]) the meridians of a triangle intersect at a point.
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$#A+1 = 139 n = 0
...pecified class of objects in this category. The categories of modules over a ring form the principal range of application of this concept.
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...the complex disc and the whole complex plane. The former is an example of a Kobayashi-hyperbolic manifold while the latter has arbitrarily large discs
Let $M$ be a [[complex manifold]], $p$ a point in $M$ and $\chi \in T_pM$ a tangent vector. Consider any [[holomorphic mapping]] $f : \Delta \rightarro
4 KB (543 words) - 09:26, 21 December 2014
$#A+1 = 70 n = 0
A [[Significance test|significance test]] for the mean value of a [[Normal distribution|normal distribution]].
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...it is a set $G$ equipped with a [[unary operation]] $g\mapsto g^{-1}$ and a partial [[binary operation]] $(g,h)\mapsto gh$ satisfying
Groupoids, as a special case of categories, play an important role in many areas of applica
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$#A+1 = 90 n = 0
A probability distribution which, for any $ n = 2, 3 \dots $
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$#A+1 = 37 n = 0
A continuous probability distribution concentrated on the positive semi-axis
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...\alpha_k|\leq|\alpha_{k+1}|$, and have no limit point in the finite plane (a necessary condition), i.e. $\lim_{k\to\infty}\alpha_k=\infty$. Then the can
...e, it suffices to take $q_k\geq k-1$. If the sequence $\{|\alpha_k|\}$ has a finite exponent of convergence
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#REDIRECT [[Extension of a field]]
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adeles (adèles) of a global field (cf.
[[Adèle|Adele]]). The set of all ideles forms a group under
4 KB (757 words) - 21:21, 22 November 2014
...n R$. Thus, $R$ determines a function (perhaps not defined everywhere) on $A$. When it satisfies $R^{-1}\circ R=\Delta$ this function is well-defined ev
...$R\subset A\times B$ between sets $A$ and $B$ such that $(a,b)\in R$ and $(a,c)\in R$ imply $b=c$.
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A rarely used translation from the Russian of the notion of an [[Exact endomo
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$#A+1 = 86 n = 0
A [[Lattice|lattice]] $ \mathbf L = ( L , \leq ) $
10 KB (1,402 words) - 08:08, 6 June 2020
$#A+1 = 123 n = 0
...y type of the knots and links. Quadratic forms of knots and links arise as a result of symmetrizing the Seifert pairing (cf. [[Seifert matrix|Seifert ma
11 KB (1,680 words) - 10:46, 20 January 2024
* A [[divisor (of an integer or of a polynomial)]]
* A [[factor algebra]]
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$#A+1 = 80 n = 1
A [[Semi-group|semi-group]] in which every element is regular (see [[Regular
10 KB (1,515 words) - 08:10, 6 June 2020
$#A+1 = 32 n = 7
...gebras (cf. [[Co-algebra|Co-algebra]]). Such an object consists, first, of a sequence $ \{ H _ {i} \} $
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$#A+1 = 20 n = 0
Consider a regular [[Martingale|martingale]] $ ( X _ {n} , {\mathcal F} _ {n} ) $,
3 KB (442 words) - 06:29, 30 May 2020