''of a function, set of values of a function, image of a function''
...$x \in X$ with $f(x) = y$. Thus, the range of values of a function is the image of its [[domain of definition]], $Y_f = f(X)$.
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...[zero-dimensional space]]. Also, every [[compact space]] is the continuous image of a closed subspace of a Cantor cube.
The terminology is slightly ambiguous: a [[dyadic space]] is a continuous image of a Cantor cube, so that "dyadic discontinuum" could also mean "totally
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...the area $S(E)$ of that part of the convex surface $F$ that has spherical image $E\subset\Omega$. This definition remains meaningful for general convex sur
...lled the spherical image of $x$. The procedure for obtaining the spherical image of a point goes under the name of spherical mapping, cf. [[Spherical map|Sp
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$#C+1 = 33 : ~/encyclopedia/old_files/data/I050/I.0500150 Image of a morphism
A concept similar to that of the image of a mapping of one set into another. However, in category theory there are
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$#C+1 = 12 : ~/encyclopedia/old_files/data/S085/S.0805800 Small image
is closed (cf. [[Closed mapping|Closed mapping]]) if and only if the small image $ f ^ { \sharp } U $
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...ts with $n=1$. After the introduction of a suitable topology, the analytic image is converted to the [[Riemann surface]] of the given function.
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...us mapping|Continuous mapping]]) of topological spaces under which the pre-image of every point is compact. Perfect mappings are akin to continuous mappings
...pre-image, and the Suslin number of the image is equal to that of the pre-image. If a completely-regular $T_1$-space is mapped onto a completely-regular $T
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...ssible to select a finite number of sets so that $y$ is located inside the image of their union. It is particularly important that the product of any collec
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The topological image of a [[Disc|disc]] (cf. also [[Disc, topological|Disc, topological]]).
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A homeomorphic image of a circle (cf. also [[Homeomorphism|Homeomorphism]]). Named after C. Jord
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A continuous image of a [[Borel set]]. Since any Borel set is a continuous
image of the set of irrational numbers, an ${\mathcal A}$-set can be defined as a
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is entirely covered by the image of the disc $ | z | < 1 $
there are points not belonging to the image only if $ f $
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...space]] such that $\pi(x)^*=\pi(x^*)$ for all $x\in A$, where $x^*$ is the image of $x$ under the involution of $A$.
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...w Y$ is a morphism of algebraic varieties, then $f(X)$ (and, moreover, the image under $f$ of any constructible subset in $X$) is a constructible subset in
...ed constructible if $h(X)$ is finite and if for any point $t\in T$ the pre-image $h^{-1}(t)$ is a constructible subset in $X$.
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...onto a topological space $Y$ which is irreducible (that is, $Y$ is not the image of any proper closed subset of $X$, cf. also [[Irreducible mapping|Irreduci
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...xtensions $A \subset \Omega$ and $B \subset \Omega$. It is the same as the image of the homomorphism $ \phi : A \otimes_{k} B \to \Omega$ that maps the tens
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...s such particularly useful for the analysis of geometrical structure in an image. It has been applied in various disciplines, such as mineralogy, medical di
...and their interrelations. In general, this procedure results in non-linear image operators, some of which will be described briefly below.
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A mapping of one topological space to another, under which the image of every closed set is a closed set. The class of continuous closed mapping
...e the above-mentioned properties. The explanation for this is that the pre-image of a point under a continuous closed mapping need not be compact, though in
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...delta$-diagonal are also metrizable. The perfect image and the perfect pre-image of a paracompact $P$-space are also paracompact $P$-spaces.
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...puter vision, aimed at detecting and characterizing discontinuities in the image domain.
...on in terms of edges is also compact in the sense that the two-dimensional image pattern is represented by a set of one-dimensional curves. For these reason
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