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denotes the [[small image]] of the set $ O _ {i} $ For this reason, fully-closed mappings can be employed to isolate fairly wide classes of compacta with non-coinciding dimensions dim and ind. Moreover,

the image of $ \sigma ^ {n} $ ...ual, cycles and boundaries are those chains which belong to the kernel and image of $ \partial ^ {n} $,

...g in numerical analysis, multi-resolution analysis and pyramidal coding in image processing. ...align="top"> M. Antonini, M. Barlaud, I. Daubechies, P. Mathieu, "Image coding using vector quantization in the wavelet transform domain" , ''IEEE

...ntinuities at boundary points of its spectrum, the combined spectra of the image of many-valued mappings, images of approximate, point or deficiency spectra ...ich implies that the essential spectra of the self-adjoint extensions of a wide class of symmetric multi-dimensional differential operators coincide. Weyl'

...essed explicitly and was not an independent object of research, although a wide range of specific functional relations were known and were studied systemat is the image of the element $ x $

...lue of this concept. On the one hand the class of perfect measures is very wide, and on the other, a number of unpleasant technical complications that occu is perfect. The image of a perfect measure $ \mu $

is the image of $ U $ ...t theorem and is a concrete realization of the Teichmüller principle for a wide class of problems (see [[#References|[1]]], [[#References|[4]]]). The Teich

...have infinite interior (for short, a Parovichenko space). This theorem had wide applications both in topology as well as in the theory of Boolean algebras. ...his implies that the ordinal space $W(\mathfrak{c}+1)$ is not a continuous image of $\omega^*$. In 1978, E.K. van Douwen and T.C. Przymusiński [[#Reference

on the terrestrial ellipsoid by its image $ d \sigma $ ...line, and the remaining meridians by curves symmetric with respect to the image of the central meridian (see, for example, Fig. f).

...ators $L$ and in [[#References|[a5]]] a characterization of the range of a wide class of multi-dimensional linear transforms, whose kernels are kernels of ...f linear transforms" A.G. Ramm (ed.) , ''Inverse Problems, Tomography and Image Processing'' , Plenum (1998) pp. 125–128</td></tr>

and the volumes of the lattices generated by the image of the $ K $- functor for a wide class of schemes. In particular, the $ K $-

...ransformation|measure preserving]]'' if for every $A_2\in\A_2$ the inverse image $A_1=f^{-1}(A_2)$ satisfies $A_1\in\A_1$, $\mu_1(A_1)=\mu_2(A_2)$. Such $f$ ...able (or equivalently, for every $\A$-measurable) function $f:X\to\R$ the image $f(X)$ contains a Borel (or equivalently, σ-compact) subset $B$ whose pre

...[[#References|[a7]]], quadratic assignment problems [[#References|[a2]]], image processing [[#References|[a5]]] and many others. In addition, implementatio

...gebraic group $G$ with respect to $S$, which consists of the fact that the image of $G_k$ under the canonical projection $G_k \to G_S$ is dense in $G_S$. Al [[#References|[2]]]). Nevertheless, for a wide class of non-simply-connected semi-simple groups, in particular, for adjoin

...rem to the case of proper morphisms of schemes and asserts that the direct image of a [[Coherent sheaf|coherent sheaf]] under such a mapping is coherent (se These theorems find application in a wide range of finiteness problems that arise in Diophantine geometry. Among them

...anifolds|topology of manifolds]], because the class of polyhedra is fairly wide. ...called a regular neighbourhood of $P$ in $Q$, and the same applies to its image under any pl-homeomorphism of $Q$ into itself that leaves $P$ invariant. Fo

...the corresponding smoothness class. A linear differential operator in the wide sense $ A: E\rightarrow F $ is equal to the image of the section $ u $

A wide class of non-strategic games can be obtained as follows. Let $ I $ image of a situation is called a play (the set of all plays is denoted by $ \ma

...$ K $-theory]], it is sometimes called topological $ K $-theory. In a wide sense, the term "K-theory" is used to denote the branch of mathematics that ...ndles (direct sums, tensor products, exterior degrees), and of the inverse image of a bundle. A second source of $ K $-theory is the connection with algeb

...s concerned only with elliptic equations. The extension of the theory to a wide class of parabolic equations was obtained by H. Bauer (1960–1963, see [[# ...is Hunt's theorem, which in its simplest version is the following: If the image of $ C _ {c} $

and its image $ f ( G) $ ...and development of the general theory of surfaces. Conformal mappings find wide application in the theory of functions, potential theory, in the solution o

The EM algorithm has enjoyed wide popularity in many scientific fields from the 1970s onwards (e.g., [[#Refer ...<td valign="top">[a30]</td> <td valign="top"> Y. Vardi, D. Lee, "From image deblurring to optimal investments: maximum likelihood solutions for positiv

is the image of $ x \in G $ ...ms of functions, in the spectral theory of operators, etc., which ensure a wide range of applications of the theory of generalized displacement operators (

...y of when a topological space from a given class can be represented as the image of a space from another given class under a continuous mapping of one kind The construction of a cohomology theory for wide classes of spaces and the construction of examples of complex topological s

The moment problem in the complex domain is the name of a wide class of interpolation problems described as follows. Let $ D $ as well as for a domain whose image $ W ( D) $

its image $ F ( \alpha ) \in H _ {\mathfrak C ^ { \prime } } ( F (A) , F (B) ) $, ...tudy. As a result of the recent theory of relative categories, which makes wide use of the techniques of adjoint functors and closed categories, a duality