...al extension of locally finite families of sets to locally finite families of open sets.
...<TD valign="top"> A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated fro
5 KB (773 words) - 22:17, 5 June 2020
...dimensional surface oriented by a (continuous) unit normal $\nu$, the flux of the vector field $v$ through the surface $\Sigma$ is given by the integral
...is computed using the [[Area formula]]. If $\Sigma$ is given by the graph of a function $f: \mathbb R^{n-1} \supset V \to \mathbb R$ with its natural or
4 KB (589 words) - 15:27, 4 February 2014
Out of 90 formulas, 90 were replaced by TEX code.-->
...near space]] over a [[Field|field]] $\mathbf{F}$. Let $L ( X )$ be the set of all linear operators with domains and ranges in $X$ and let
10 KB (1,502 words) - 22:40, 12 December 2020
...e set of points at which $f$ vanishes (cf. [[Support of a function|Support of a function]]). For example, $\mathop{\mathrm{supp}} x = \mathbf{R}^1$, $\ma
...is the set of those (and only those) points such that in any neighbourhood of them the generalized function is not equal to a $C^\infty$-function. For ex
3 KB (450 words) - 09:18, 12 August 2022
...ch can be regarded as a direct generalization of the [[Fundamental theorem of calculus]], is often referred to as:
...ield are denoted by $v_1, \ldots, v_n$, then the [[Divergence|divergence]] of $v$ is given by the function
6 KB (926 words) - 13:28, 26 February 2014
...t [[Hausdorff space|Hausdorff space]] is called a paracompactum. The class of paracompacta is very extensive — it includes all metric spaces (Stone's t
...of the requirements assumed in the theory of manifolds is the requirement of paracompactness, which is not superfluous since there exist non-paracompact
9 KB (1,401 words) - 14:04, 30 July 2014
...sly-differentiable vector function defined on the closure $ \overline{G} $ of a two-dimensional Jordan-measurable domain $ G $ lying in the plane with Ca
...$ F(x(u,v),y(u,v),z(u,v)) $, then the following defines a surface integral of the first kind (or a integral over the surface area):
11 KB (1,911 words) - 18:57, 1 December 2016
of a universal fibre bundle $ \xi = ( E _ {0} , p _ {0} , B _ {0} ) $.
The universality of the bundle $ \xi $
9 KB (1,417 words) - 20:39, 23 December 2023
$#C+1 = 179 : ~/encyclopedia/old_files/data/A011/A.0101370 Algebra of functions,
realized as an algebra of continuous functions on the space of maximal ideals $ \mathfrak M $.
11 KB (1,877 words) - 16:10, 1 April 2020
This page is a copy of the article [[Weyl module]] in order to test [[User:Maximilian_Janisch/late
...roup this reduction is carried out with respect to the field of definition of the group.
32 KB (4,878 words) - 13:44, 17 October 2019
...nces|[2]]]) and in studying the singularities of the fundamental solutions of hyperbolic equations (see [[#References|[1]]], [[#References|[2]]], [[#Refe
dimensional [[Lagrangian manifold|Lagrangian manifold]] of class $ C ^ \infty $
24 KB (3,360 words) - 19:39, 5 June 2020
Out of 445 formulas, 443 were replaced by TEX code.-->
...roup this reduction is carried out with respect to the field of definition of the group.
33 KB (5,081 words) - 10:26, 11 November 2023
...of a certain function algebra $ A $ (cf. [[Algebra of functions|Algebra of functions]]) into the algebra $ L ( X) $
of continuous linear operators on a topological vector space $ X $.
11 KB (1,521 words) - 02:23, 16 June 2022
...t of a [[Residue of an analytic function|residue of an analytic function]] of one complex variable to several complex variables. Let $ X $
be an analytic submanifold of complex codimension one and let $ \omega ( x) $
11 KB (1,662 words) - 08:11, 6 June 2020
My [http://user.math.uzh.ch/delellis/ homepage] at the University of Zuerich.
[[Variational calculus|calculus of variations]], [[Geometric_measure_theory | geometric measure theory]] and [
11 KB (1,076 words) - 07:40, 12 July 2014
...e introduction of a canonical structure. M. Sato has constructed the sheaf of micro-functions on the cotangent sphere bundle $ S ^ {*} M $
of the base space $ M $
13 KB (1,805 words) - 19:06, 9 January 2024
Out of 227 formulas, 227 were replaced by TEX code.-->
...rier hyperfunctions was proposed by M. Sato at the same time as his theory of hyperfunctions, in which the transformed objects can be interpreted natural
26 KB (3,903 words) - 17:01, 1 July 2020
A partial differential equation (system) of the form
is a multi-index (a set of non-negative integers), $ | \alpha | = \sum {\alpha _ {i} } $,
18 KB (2,569 words) - 22:17, 5 June 2020
A theory studying continuous families of objects in algebraic geometry.
be a class of objects in algebraic geometry (varieties, schemes, vector bundles, etc.) on
16 KB (2,402 words) - 11:49, 16 December 2019
This page is a copy of the article [[Moduli theory]] in order to test [[User:Maximilian_Janisch/la
A theory studying continuous families of objects in algebraic geometry.
16 KB (2,379 words) - 13:44, 17 October 2019