''$A$ in a topological space $X$''
...in $X$ are closed. The pseudo-character $\psi(x,X)$ of a point $x\in X$ in a topological space $X$ is understood to be the pseudo-character $\psi(\{x\},
2 KB (346 words) - 13:09, 27 September 2014
''in a Euclidean space $E^n$''
...ty, it is perfect and has the cardinality of the continuum. The concept of a condensation point can be generalized to arbitrary topological spaces.
861 bytes (136 words) - 09:56, 26 March 2023
$#A+1 = 37 n = 0
$#C+1 = 37 : ~/encyclopedia/old_files/data/I051/I.0501550 Integral of a differential equation
5 KB (803 words) - 12:07, 31 March 2024
...mposition of a '''signed''' measure we refer to [[Jordan decomposition (of a signed measure)]].
...e $p\in [0,1]$, $\mu_a$ is an atomic probability measure and $\mu_{na}$ is a nonatomic probability measure. The decomposition into atomic and nonatomic
532 bytes (81 words) - 10:44, 17 September 2012
The collection of points at which $K$ is a [[Smooth continuum|smooth continuum]].
103 bytes (18 words) - 13:42, 29 April 2014
$#A+1 = 17 n = 0
$#C+1 = 17 : ~/encyclopedia/old_files/data/P072/P.0702420 Perturbation of a linear system
3 KB (437 words) - 07:39, 26 February 2022
''$S$ in a class of semi-groups $\Sigma$''
...rtain simple representations by union, multiple repetition, restriction to a subset, and by the operation of [[imbedding of semi-groups]].
4 KB (637 words) - 19:07, 20 March 2018
$#A+1 = 34 n = 0
...34 : ~/encyclopedia/old_files/data/D030/D.0300410 Decimal approximation of a real number
3 KB (445 words) - 17:32, 5 June 2020
A projective system of topological spaces that is associated with a [[Topologized category|topologized category]] and which makes it possible t
provided with a [[Grothendieck topology|Grothendieck topology]] $ \tau $
6 KB (842 words) - 13:07, 15 December 2019
Let $C$ be a smooth [[Jordan curve|Jordan curve]] (of class $C ^ { 3 }$) in the complex
...a2]]]. In some sense, $\lambda$ is a measure for the deviation of $C$ from a circle. $\lambda$ is invariant under Möbius transformations (cf. also [[Fr
7 KB (989 words) - 20:48, 23 January 2024
...ice|Banach lattice]] (cf. also [[Riesz space|Riesz space]]) of measures on a [[Measurable space|measurable space]] $ ( \Omega, {\mathcal F} ) $,
is a set of probability measures on $ ( \Omega, {\mathcal F} ) $.
9 KB (1,287 words) - 16:56, 1 July 2020
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42 bytes (4 words) - 20:28, 8 November 2016
''$V$ of a representation $T$ of a Lie group $G$''
A vector $\xi \in V$ for which the mapping
3 KB (401 words) - 18:39, 17 October 2016
$#A+1 = 24 n = 0
...: ~/encyclopedia/old_files/data/W097/W.0907400 Weierstrass conditions (for a variational extremum)
3 KB (508 words) - 08:28, 6 June 2020
...armonic conformal mapping $X : M \rightarrow {\bf R} ^ { n }$ then defines a [[Minimal surface|minimal surface]] in ${\bf R} ^ { n }$, $n \geq 3$ (cf. a
is a holomorphic $1$-form on $M$. Hence any (branched) minimal surface in ${\bf
4 KB (595 words) - 16:57, 1 July 2020
...f a [[compact group]] into the group of continuous linear automorphisms of a (complex) Banach space that is continuous with respect to the strong operat
be a compact group, let $ V $
5 KB (636 words) - 06:35, 19 May 2024
...tion of a '''nonnegative measure''' we refer to [[Jordan decomposition (of a measure)]].
...a [[Algebra of sets|σ-algebra]] $\mathcal{B}$ of subsets of a set $X$ and a [[Signed measure|signed measure]]
3 KB (419 words) - 12:56, 2 December 2012
$#A+1 = 26 n = 0
...1 = 26 : ~/encyclopedia/old_files/data/P110/P.1100220 Primitive element in a co\AAhalgebra
2 KB (345 words) - 17:37, 16 December 2020
''dimension of a poset''
...X,{\le})$ be a [[partially ordered set]]. A linear extension $L$ of $P$ is a total ordering $\le_1$ (see also [[Totally ordered set]]) on $X$ such that
2 KB (402 words) - 15:27, 10 January 2016
is $\sum_{|\alpha|=m}a_\alpha D^\alpha$. The principal part of a differential operator is sometimes defined by the introduction of supplemen
Further, a constant-coefficient differential operator $L$ in $\mathbf R^n$ is said to
2 KB (249 words) - 14:26, 8 August 2014
A spectral set of an operator $A$ on a normed space is a subset $S\subset\mathbf C$ such that
$$\|p(A)\|\leq\sup\{|p(z)|:z\in S\}$$
2 KB (295 words) - 15:46, 29 December 2018
...prime if and only if the [[principal ideal]] generated by this element is a [[prime ideal]].
<TR><TD valign="top">[2]</TD> <TD valign="top"> A.G. Kurosh, "Lectures on general algebra" , Chelsea (1963) (Translated f
1 KB (252 words) - 16:49, 13 August 2023
...} $ is a [[Flag|flag]] in a finite-dimensional vector space $ V $ over a field $ K $ , then $$
...nted by triangular matrices with ones on the main diagonal. If $ F $ is a complete flag (that is, if $ \mathop{\rm dim}\nolimits \ V _{k} = k $ )
5 KB (803 words) - 18:12, 12 December 2019
$#A+1 = 19 n = 0
$#C+1 = 19 : ~/encyclopedia/old_files/data/A110/A.1100440 Ahlswede\ANDDaykin inequality,
4 KB (523 words) - 19:25, 4 April 2020
$#A+1 = 58 n = 0
A domain in the $ ( n + 1 ) $-
8 KB (1,167 words) - 20:20, 10 January 2024
illumination of statistics as a coherent mathematical discipline.
becoming a student of the influential Swedish mathematician Mittag-Leffler and
13 KB (2,000 words) - 18:58, 5 March 2024
$#A+1 = 529 n = 1
''over a [[Topological field|topological field]] $ K $''
41 KB (6,085 words) - 08:26, 6 June 2020
A point on a regular surface at which the osculating paraboloid is an elliptic paraboloi
holds. In a neighbourhood of an elliptic point the surface is locally convex.
452 bytes (74 words) - 19:12, 12 April 2014
...r instance, on a hyperboloid of revolution the rectilinear generators form a rhombic net.
416 bytes (64 words) - 22:01, 7 July 2014
$#A+1 = 39 n = 0
...clopedia/old_files/data/G044/G.0404960 Graph, numerical characteristics of a
5 KB (780 words) - 20:06, 15 March 2023
$#A+1 = 29 n = 0
One of the first concepts of a derivative in an infinite-dimensional space. Let $ I ( y) $
3 KB (409 words) - 19:40, 5 June 2020
A homogeneous space $ M $
of a connected solvable Lie group $ G $ (cf. [[Lie group, solvable|Lie group,
5 KB (755 words) - 07:05, 12 July 2022
A field with a finite number of elements. First considered by E. Galois [[#References|[1]]
...extensions of any Galois field within its fixed algebraic closure is such a lattice.
4 KB (749 words) - 18:32, 2 November 2014
...roup in $ \mathop{\rm GL}\nolimits (n,\ k) $ . All closed subgroups of a real or $ p $ -adic analytic group are analytic, and each continuous homo
...nces|[1]]], but a Lie group is usually understood in the narrower sense of a real analytic group [[#References|[2]]], [[#References|[3]]] (cf. [[Lie gro
6 KB (902 words) - 17:45, 12 December 2019
...[[#References|[a1]]] to certain convergent formal power series rings over a field of non-zero characteristic.
The following assertion holds: A Noetherian local ring has AP if and only if it is excellent and Henselian.
16 KB (2,444 words) - 18:28, 7 October 2025
$#A+1 = 11 n = 1
''of a function $ f $
3 KB (417 words) - 20:00, 15 January 2024
A mapping of a plane $\pi$ into a plane $\pi_1$ under which each point $M$ in $\pi$ is put into correspondenc
...aximal dimension not having points in common with $V$ or $V_1$. Let $U$ be a subspace contained in $V$, let $W$ be the subspace of minimal dimension con
2 KB (359 words) - 22:17, 11 April 2014
Henry and Mary Graunt. His father was a draper who had moved to London
He was made a Freeman of the Drapers'
7 KB (1,078 words) - 09:01, 18 March 2023
$$a(\lambda)=M\{f(x)e^{-i\lambda x}\},$$
<TR><TD valign="top">[a1]</TD> <TD valign="top"> A.S. Besicovitch, "Almost periodic functions" , Cambridge Univ. Press (193
1,013 bytes (164 words) - 16:21, 28 March 2025
...le structures, and with spectral lines present in the light originating in a distant part of the Universe.
...{ t t }$. Separation of variables $u ( x , t ) = v ( x ) w ( t )$ leads to a pair of equations $v _ { x x } = \lambda v$, $w _ { t t } = \lambda w$.
9 KB (1,325 words) - 18:26, 21 October 2025