$#C+1 = 24 : ~/encyclopedia/old_files/data/F041/F.0401930 Fully\AAhclosed mapping
A continuous mapping $ f: X \rightarrow Y $
2 KB (274 words) - 11:41, 18 February 2022
...anach space]] $X$ onto all of a Banach space $Y$ is an [[Open mapping|open mapping]], i.e. $A(G)$ is open in $Y$ for any $G$ which is open in $X$. This was pr
The conditions of the open-mapping theorem are satisfied, for example, by every non-zero continuous linear fun
2 KB (286 words) - 15:25, 27 August 2014
''(inverse operator) of a single-valued onto mapping (operator) $ f: M \to f[M] $''
A single-valued mapping $ g $ such that
4 KB (752 words) - 03:29, 9 January 2017
...ndition that its restriction to the fibre $S$ over $G_{X}$ is the identity mapping $S \rightarrow S$ (cf. also [[Equivariant cohomology|Equivariant cohomology
iv) there is an equivariant mapping $\pi : G ( S ) \rightarrow G ( x )$ that is the identity on $G ( x )$ and i
11 KB (1,819 words) - 15:30, 1 July 2020
...the given variety containing an infinite free system of generators: Every mapping from the set of free generators into an arbitrary ring of the variety can b
4 KB (701 words) - 17:01, 23 November 2023
Since a harmonic form is closed, de Rham's theorem generates a natural mapping of the space $ H ^ {p} ( M) $
It follows from the [[Hodge theorem|Hodge theorem]] that this mapping is an isomorphism. In particular, harmonic functions, i.e. harmonic forms o
8 KB (1,166 words) - 19:43, 5 June 2020
...ector space structure, that is, the following axioms are satisfied: 1) the mapping $ ( x _ {1} , x _ {2} ) \rightarrow x _ {1} + x _ {2} $,
is continuous; and 2) the mapping $ ( k, x) \rightarrow kx $,
41 KB (6,085 words) - 08:26, 6 June 2020
A mapping of the group $ G $
a continuous mapping of $ G $
20 KB (2,775 words) - 16:40, 31 March 2020
...the edges between the $j$th and the $(j+1)$st row describe the connecting mapping $A_j\rightarrow A_{j+1}$. By the facts mentioned above, the construction an
is a (positive) linear mapping $ \tau : A \rightarrow \mathbf C $
12 KB (1,766 words) - 06:39, 26 March 2023
...lled Leray mapping (or Leray section) for $D$, that is, a (differentiable) mapping $s = ( s _ { 1 } , \dots , s _ { n } ) : \partial D \times D \rightarrow \m
...\ldots , \partial r / \partial \zeta _ { n } ( \zeta ) )$ defines a Leray mapping that is holomorphic in $z$. The associated kernel $K ( s _ { r } )$ is then
15 KB (2,167 words) - 16:10, 11 February 2024
...d onto mappings which preserve distance (cf. [[Isometric mapping|Isometric mapping]]). Such properties include completeness, boundedness, total boundedness, a
...$. The trivial metric leads to the trivial topology, in which all sets are closed.
33 KB (5,289 words) - 19:37, 25 March 2023
...algebraic curve means an irreducible algebraic curve over an algebraically closed field.
is a polynomial with coefficients from an algebraically closed field $ k $ .
22 KB (3,307 words) - 17:02, 17 December 2019
4) As a result of analytic continuation along a closed path $\gamma$ the fundamental matrix $X(t)$ is multiplied by a constant mat
5) Let the function $z=\phi(t)$ be a conformal mapping of the upper half-plane $\operatorname{Im} t > 0$ onto the interior of a po
16 KB (2,410 words) - 11:15, 28 January 2020
...ences|[a7]]] calls a Cartesian closed category (cf. also [[Closed category|Closed category]]). These equations will ensure that there is exactly one arrow $A
...s with surjective pairing, which turns out to be equivalent to a Cartesian closed category, see [[#References|[a12]]] and [[#References|[a6]]]. Like conjunct
24 KB (4,067 words) - 20:57, 21 December 2017
...rices, the set of all solutions can be parametrized by a fractional-linear mapping of which the coefficients can be constructed explicitly in terms of the giv
...iss, "Quasitriangular subalgebras of semifinite von Neumann algebras are closed" ''J. Funct. Anal.'' , '''107''' (1992) pp. 387–401</TD></TR><TR><TD v
14 KB (2,045 words) - 15:19, 28 February 2022
...ructured as a projection of a direct product with smooth factors) analytic mapping
is an analytic deformation, then any analytic mapping
41 KB (5,916 words) - 11:24, 26 March 2023
...ch such curve may be extended in both directions up to the boundary of any closed subregion lying completely in $ D $
...to carry out the integration of equations in quadratures, i.e. to obtain a closed formula yielding (in explicit, implicit or parametric form) an expression f
33 KB (4,933 words) - 01:50, 23 January 2022
...w of motion (3) is given, the state of the system at any moment of time is fully determined by its initial state. Generally speaking, the solution need not
and one obtains a mapping $ S _ {t} $
27 KB (4,058 words) - 19:36, 5 June 2020
...t $T$ of formulas is a theory of a deductive system $\mathcal{D}$ if it is closed under consequence, i.e., $\varphi \in T$ whenever $\Gamma \subset T$ and $\
...le$ is a model of $\mathcal{D}$; thus $F$ is a filter if and only if it is closed under consequence in the sense that, if $\Gamma \vdash_{\mathcal{D}} \varph
76 KB (11,425 words) - 02:12, 15 February 2024
...heorem of analysis stating that every real-valued continuous function on a closed bounded set in $ \mathbf R ^ {n} $
...system of concepts every intuitionistic real-valued function defined on a closed segment is uniformly continuous. Intuitionistic mathematics is a well-devel
24 KB (3,697 words) - 22:13, 5 June 2020