...all inverse images of points are finite. Mappings under which the inverse image of every compact set is compact are called $ k $-
is open if and only if its complete inverse image $ f ^ { - 1 } ( V) $
6 KB (910 words) - 07:59, 6 June 2020
A mapping of one topological space into another under which the image of every open set is itself open.
...by a complete metric. If a [[Paracompact space|paracompact space]] is the image of a [[Complete metric space|complete metric space]] under a continuous ope
3 KB (511 words) - 08:04, 6 June 2020
...f the $2$-dimensional sphere $S^2$; also, every cactoid is a monotone open image of $S^2$.
460 bytes (78 words) - 22:20, 1 November 2014
...tremal disconnectedness is not preserved by perfect mappings. However, the image of an extremally-disconnected space under a continuous open mapping is an e
2 KB (261 words) - 19:42, 14 April 2017
...et: \(X\) satisfies the first axiom of countability; \(X\) is a continuous image of an ordered compactum; \(X\) is hereditarily normal; \(X\) is hereditaril
3 KB (415 words) - 20:38, 2 January 2021
A '''Suslin space''' is a continuous image of a Polish space.
473 bytes (65 words) - 19:36, 1 January 2021
...rplane section in $\PP^n$. The Veronese mapping is a closed imbedding; its image $v_m(\PP^n)$ is called a Veronese variety, and is defined by the equations
in $\PP^n$ its image with respect to the Veronese mapping $v_m$ is the intersection of the Veron
2 KB (408 words) - 23:35, 22 October 2018
a pre-image $ x \in L _ {n} $
will then be the image of an element $ z \in Z _ {n-} 1 ( K _ {\mathbf . } ) $
2 KB (254 words) - 22:11, 5 June 2020
..., depending on the orientation. Certain knots can differ from their mirror image owing to the fact that their branched coverings are asymmetric varieties.
591 bytes (78 words) - 06:09, 23 April 2023
...nding to the deformation over a principal base, as well as to the Clifford image of the asymptotic lines of a surface in an elliptic space (which is the [[R
5 KB (766 words) - 12:40, 2 November 2014
It follows from the Tarski–Seidenberg theorem that the image under a polynomial mapping $ \mathbf R ^ {n} \rightarrow \mathbf R ^ {m
...t on a real-analytic manifold is, by definition, a set that is locally the image of a semi-analytic set under an analytic mapping. The points of a subanalyt
4 KB (573 words) - 18:05, 26 January 2022
...ts of the kernel $\ker d$ are known as ''cycles''; and the elements of the image $\mathrm{im}\, d$ are called ''boundaries''. The ''homology'' of $C$ is th
513 bytes (78 words) - 14:52, 8 April 2023
...rithmic capacity|logarithmic capacity]]. As an example, any function whose image does not contain a disc of a fixed radius $\epsilon > 0$ centred at $a +
...proved that an analytic function is in $\operatorname{BMOA}$ provided its image [[Riemann surface]] (viewed as spread out over the complex plane) has the f
5 KB (707 words) - 19:01, 22 January 2024
The Lindelöf principle states that under these conditions: 1) the inverse image $ \widetilde{D} _ \rho $
lies inside the inverse image $ D _ \rho $
6 KB (873 words) - 22:16, 5 June 2020
...an open connected set. The basic property here is that of openness of the image, which follows from Rouché's theorem or from the principle of the argument
say, then the image $ f ( X) \subset Y $
3 KB (457 words) - 08:07, 6 June 2020
..., touching an arc of the circle $L$ (the image of $K$) at that point; this image is represented in Fig. band is the Zhukovskii profile.
4 KB (542 words) - 19:58, 4 January 2024
A continuous mapping $h : f(X) \rightarrow X$ of the image $f(X)$ of a continuous mapping $f : X \rightarrow Y$ of topological spaces
294 bytes (55 words) - 19:51, 22 October 2016
is always the image of some horizontal distribution $ \Delta $
is obtained as the image $ \pi ^ {*} \overline \Delta \; $,
3 KB (524 words) - 17:36, 13 January 2021
such that the image of any set $ U $
while the inverse image $ f ^ { - 1 } ( y) $
2 KB (327 words) - 22:13, 5 June 2020
...z$ vary monotonically on the image of the trajectory in $|z|<\alpha$. Each image of a trajectory twists around the point $z=0$ and behaves asymptotically li
...ha$ in the other direction. The modulus of $z$ varies monotonically on the image of the trajectory in $|z|<\alpha$. Different images of trajectories have di
6 KB (960 words) - 21:47, 1 January 2019