...closed if it is bounded by the two plane domains interior to the curves of intersection of planes $\pi_1$ and $\pi_2$ with it.
353 bytes (61 words) - 16:40, 11 April 2014
$#C+1 = 17 : ~/encyclopedia/old_files/data/I052/I.0502010 Intersection index (in algebraic geometry)
The number of points in the intersection of $ n $
2 KB (289 words) - 06:42, 29 December 2021
...ll these sets (the set of elements common to all $A_\alpha$) is called the intersection of these sets.
The intersection of these sets is denoted by $\bigcap A_\alpha$.
453 bytes (76 words) - 19:46, 8 November 2014
- the [[centroid]] (''i.e.'' the centre of mass), the common intersection point of the three medians (see [[Median (of a triangle)]]);
- the incentre, the common intersection point of the three bisectrices (see [[Bisectrix|Bisectrix]]) and hence the
2 KB (333 words) - 08:29, 23 November 2023
...$A_i = \{ n \in \mathbf{Z} : n > i \}$ is centred; any family in which the intersection of all members is not empty is centred. Every finite centred family of sets
...s compact if and only if every centred family of closed sets has non-empty intersection. Centred families of closed sets in a topological space are used for the co
2 KB (253 words) - 21:48, 17 December 2015
in the same plane defined as follows: 1) the intersection of $ G ^ {*} $
is either empty or is the entire circle, depending on whether the intersection of $ G $
2 KB (241 words) - 16:44, 4 June 2020
...point $H$ of intersection of the altitudes of a triangle, the point $S$ of intersection of its [[Median (of a triangle)|median]]s (the [[centroid]]), and the centr
730 bytes (113 words) - 20:16, 16 January 2016
In a topological space $X$ a subset which is the countable intersection of open sets. See [[Borel set]] and also [[F-sigma]].
193 bytes (29 words) - 18:22, 18 August 2012
...ion of all modular maximal right ideals (cf. [[Modular ideal]]); it is the intersection of all modular maximal left ideals; it contains all quasi-regular one-sided
...adical $J(A)$ is the intersection of all right maximal ideals and also the intersection of all left maximal ideals. Nakayama's lemma says that if $M$ is a finitely
3 KB (444 words) - 06:49, 21 October 2017
...$ denote the operations of [[union of sets|union]], [[intersection of sets|intersection]], [[Difference of two sets|difference]], and [[complementation]] of sets,
...{P}(X)$ of a set $X$ (the set of subsets of $X$), in contrast to union and intersection. This ring is the same as the ring of $\mathbb{Z}/2\mathbb{Z}$-valued funct
2 KB (273 words) - 08:47, 29 April 2023
The ellipse of least surface area obtained as the intersection of a one-sheet [[Hyperboloid|hyperboloid]] with a plane perpendicular to it
145 bytes (22 words) - 17:06, 7 February 2011
An ideal $I$ of a ring $R$ which cannot be expressed as the intersection of a right [[fractional ideal]] $r(I,A)$ and an ideal $B$, each strictly la
...or left and right fractional ideals, and that every ideal decomposes as an intersection of finitely many indecomposable ideals. Then for every ideal $Q$ there exis
2 KB (297 words) - 19:23, 5 October 2017
...rsection of the bisectrix of the angle $C$ with $AB$, and the point $L$ of intersection of the bisectrix of the external angle $C$ with $AB$ forms a [[harmonic qua
1 KB (240 words) - 14:00, 12 November 2023
The intersection $M$ of all subspaces containing $A$. The set $M$ is also called the subspac
...l of a set $A$ is called the ''[[linear closure]]'' of $A$; it is also the intersection of all closed subspaces containing $A$.
855 bytes (145 words) - 08:49, 26 November 2023
...all maximal modular right ideals of an associative ring coincides with the intersection of all maximal left modular ideals and is the [[Jacobson radical]] of the r
867 bytes (141 words) - 16:16, 11 September 2016
...of these is the point of intersection of $l$ and $l'$, then the points of intersection of $AB'$ and $A'B$, $BC'$ and $B'C$, $AC'$ and $A'C$ are collinear.
1,003 bytes (158 words) - 12:52, 10 August 2014
...posite to this vertex at a point on the line passing through the points of intersection of the remaining pairs of non-adjacent sides of the pentagon (see Fig. b).
...t $C$ and $D$ with the sides $AD$ and $BC$, respectively, and the point of intersection of $AB$ and $CD$ are collinear (see Fig. c).
3 KB (409 words) - 21:10, 11 April 2014
...d $L^{i+1} = L L^i$, $i \ge 0$, with $\lambda$ denoting the empty string), intersection with [[regular language]]s, morphisms (non-erasing in the context-sensitive
1) union, Kleene ${+}$, non-erasing morphisms, inverse morphisms, and intersection with regular languages is closed under concatenation;
4 KB (577 words) - 21:45, 1 April 2018
The point of intersection of the lines joining the vertices of a triangle to the points where the sid
343 bytes (55 words) - 17:25, 7 February 2011
$#C+1 = 57 : ~/encyclopedia/old_files/data/I052/I.0502020 Intersection index (in homology)
...erizing the algebraic (i.e. including orientation) number of points in the intersection of two subsets of complementary dimensions (in [[General position|general p
4 KB (597 words) - 22:13, 5 June 2020
...f a given ring is a [[lattice]], $S(R)$, with respect to the operations of intersection and join of subrings. The set of ideals (cf. [[Ideal]]) of this ring forms
2 KB (297 words) - 17:54, 3 January 2016
...und the circles $c$ and $c'$ while preserving the distance $TT'$, i.e. the intersection line will be an ellipse ($MF'+MF=TT'$, $MF'=MT'$ and $MF=MT$). In the case
1 KB (207 words) - 11:21, 26 March 2023
...sets in $X$ with empty intersection contains a finite subfamily with empty intersection; 2) every [[Ultrafilter|ultrafilter]] in $X$ is convergent; and 3) every op
1 KB (185 words) - 20:48, 16 October 2014
...dges that have no common vertex are called opposite; the points $P,Q,R$ of intersection of the opposite edges are called diagonal points.
If $S$ and $T$ are the points of intersection of the line $PQ$ with the lines $AD$ and $BC$, then the four points $P,Q,S,
1 KB (226 words) - 16:52, 8 April 2023
An ideal $I$ in a ring which cannot be expressed as the intersection of two strictly larger ideals: that is, $I = J \cap K \Rightarrow I=J \ \te
332 bytes (55 words) - 18:11, 14 November 2023
The [[Closure of a set|closure]] of the [[linear hull]] of $A$; the intersection of all closed linear subspaces of $T$ containing $A$.
190 bytes (34 words) - 22:26, 10 January 2016
...ction, respectively union, of a finite number, and the union, respectively intersection, of any number of elements of $\mathfrak G$, respectively $\mathfrak F$, is
1 KB (214 words) - 06:39, 13 October 2014
...n $R$ is the smallest transitive relation containing $R$: equivalently the intersection of all transitive relations containing $R$ (there exists at least one such,
1 KB (245 words) - 19:34, 17 November 2023
The point of intersection of the straight lines joining the vertices of a triangle to the points at w
659 bytes (97 words) - 13:57, 8 April 2023
...with as simplices the finite non-empty subsets of $\alpha$ with non-empty intersection. In particular, the vertices of $K(\alpha)$ are the non-empty elements of $
255 bytes (37 words) - 12:24, 12 April 2014
A point $x$ such that every neighbourhood of it has non-empty intersection with $A$. The set of all proximate points forms the closure $[A]$, or $\bar
286 bytes (52 words) - 17:15, 11 April 2014
...ions containing the zero and identity operations and which is closed under intersection of projections (i.e., taking the greatest lower bound) and union of project
1 KB (219 words) - 14:33, 24 September 2014
...nvex polygon is the [[convex hull]] of a finite set of points and also the intersection of a finite number of closed half-spaces.
337 bytes (55 words) - 20:12, 9 November 2014
...r contact with $S$ at $x$ one can select the quadrics in which the line of intersection with $S$ has a singular point $x$ with three coincident tangents. On the su
2 KB (240 words) - 08:52, 8 April 2023
...h (possibly empty), and a subset $F\subset X$ is closed if and only if its intersection with every simplex is closed. Every simplicial space is a [[Cellular space|
2 KB (252 words) - 16:30, 9 April 2014
is a vector group if and only if its partial order is an intersection of total orders on $ G $.
where this intersection is taken over all combinations of signs $ \epsilon _ {i} = \pm 1 $,
1 KB (226 words) - 08:28, 6 June 2020
...solutely convex if and only if for any elements $g\not\in H$, $a\in H$ the intersection $S(g)\cap S(ga)$ is non-empty, where $S(x)$ is the minimal invariant sub-se
2 KB (249 words) - 16:16, 12 April 2014
The minimal [[Convex set|convex set]] containing $M$; it is the intersection of all convex sets containing $M$. The convex hull of a set $M$ is denoted
The closure of the convex hull is called the closed convex hull. It is the intersection of all closed half-spaces containing $M$ or is identical with $E^n$. The pa
2 KB (274 words) - 20:10, 9 November 2014
...of a set $M$ in a topological space $X$ is a point $x\in X$ such that the intersection of $M$ with any neighbourhood of $x$ has the same cardinality as the entire
461 bytes (70 words) - 19:37, 15 April 2018
...the intersection points of the opposite sides, and let $C$ and $D$ be the intersection points of the diagonals $SQ$ and $PR$ of $PQRS$ with the straight line $AB$
2 KB (278 words) - 13:42, 29 April 2014
...mension theory and the theory of multiplicities (and [[Intersection theory|intersection theory]]), cf. [[#References|[a1]]], [[#References|[a2]]], [[#References|[a
6 KB (934 words) - 22:15, 5 June 2020
A point $a\in A$ such that the intersection of some [[Neighbourhood|neighbourhood]] of $a$ with $A$ consists of the poi
608 bytes (90 words) - 08:27, 23 November 2023
...utions is, by definition, the [[Intersection index (in algebraic geometry)|intersection index (in algebraic geometry)]] of the hypersurfaces \eqref{*} at the respe
2 KB (268 words) - 15:02, 14 February 2020
...[[injective hull]] $E$ of the module $M/N$ (cf. [[Injective module]]) the intersection of the kernels of the homomorphisms from $E$ into $E_1$ is trivial. Another
3 KB (455 words) - 19:51, 5 October 2017
...the complex [[projective plane]] is an asymmetric variety, since the self-intersection of the complex straight line is $+1$ or $-1$, depending on the orientation.
591 bytes (78 words) - 06:09, 23 April 2023
A subset of $X$ that is the intersection of an [[open set]] and a [[closed set]] in $X$: equivalently, a subset that
510 bytes (75 words) - 18:35, 19 November 2016
Two closed curves obtained as the intersection of two cylinders the axes of which intersect at right angles. The parametri
379 bytes (73 words) - 09:40, 5 August 2014
...mension $k\times l$, where $1<k<m$, $1<l<n$, formed by the elements at the intersection of $k$ specified rows and $l$ specified columns of $A$ with retention of th
442 bytes (80 words) - 19:36, 11 December 2015
A submodule $E$ of $M$ is essential it has a non-trival intersection with every non-trivial submodule of $M$: that is, $E \cap L = 0$ implies $L
480 bytes (76 words) - 14:23, 12 November 2023
...each point $M$ in $\pi$ is put into correspondence with the point $M_1$ of intersection of the straight line $SM$ with $\pi_1$ (if $SM$ is not parallel to $\pi_1$,
...subspace of minimal dimension containing $U$ and $T$ and let $U_1$ be the intersection of $W$ and $V_1$.
2 KB (359 words) - 22:17, 11 April 2014